Update to v1.1

Wrong factor in (13)

Typos

Update style files, add DOIs to the bibliography

BBlog.sty

@@ -4,7 +4,7 @@
 
 %% length used to display the bibliography
 \newlength{\rw}
-\setlength{\rw}{1.5cm}
+\setlength{\rw}{1.75cm}
 
 %% read header
 \IfFileExists{header.BBlog.tex}{\input{header.BBlog}}{}
@@ -28,6 +28,14 @@
 %% an empty definition for the aux file
 \def\BBlogcite#1{}
 
+%% an entry
+\long\def\BBlogentry#1#2#3{
+  \hrefanchor
+  \outdef{label@cite#1}{#2}
+  \parbox[t]{\rw}{[\cite{#1}]}\parbox[t]{\colw}{#3}\par
+  \bigskip
+}
+
 %% display the bibliography	
 \long\def\BBlography{
   \newlength{\colw}

Gallavotti_Jauslin_2015.tex

@@ -32,14 +32,14 @@ The $s-d$ model describes a chain of spin-1/2 electrons interacting magnetically
 
 \hugeskip
 
-\indent The $s-d$ model was introduced by Anderson [\cite{andSO}] and used by Kondo [\cite{konSF}] to study what would subsequently be called the {\it Kondo effect}. It describes a chain of electrons interacting with a fixed spin-1/2 magnetic impurity. One of the manifestations of the effect is that when the coupling is anti-ferrmoagnetic, the magnetic susceptibility of the impurity remains finite in the 0-temperature limit, whereas it diverges for ferromagnetic and for vanishing interactions.\par
+\indent The $s-d$ model was introduced by Anderson [\cite{An61}] and used by Kondo [\cite{Ko64}] to study what would subsequently be called the {\it Kondo effect}. It describes a chain of electrons interacting with a fixed spin-1/2 magnetic impurity. One of the manifestations of the effect is that when the coupling is anti-ferrmoagnetic, the magnetic susceptibility of the impurity remains finite in the 0-temperature limit, whereas it diverges for ferromagnetic and for vanishing interactions.\par
 
-\indent A modified version of the $s-d$ model was introduced by Andrei [\cite{andEZ}], which was shown to be exactly solvable by Bethe Ansatz. In [\cite{bgjOFi}], a hierarchical version of Andrei's model was introduced and shown to exhibit a Kondo effect. In the present letter, we show how the argument can be adapted to the $s-d$ model.\par
+\indent A modified version of the $s-d$ model was introduced by Andrei [\cite{An80}], which was shown to be exactly solvable by Bethe Ansatz. In [\cite{BGJ15}], a hierarchical version of Andrei's model was introduced and shown to exhibit a Kondo effect. In the present letter, we show how the argument can be adapted to the $s-d$ model.\par
 
-\indent We will show that in the hierarchical $s-d$ model, the computation of the susceptibility reduces to iterating an {\it explicit} map relating 6 {\it running coupling constants} (rccs), and that this map can be obtained by restricting the flow equation for the hierarchical Andrei model [\cite{bgjOFi}] to one of its invariant manifolds. The physics of both models are therefore very closely related, as had already been argued in [\cite{bgjOFi}]. This is particularly noteworthy since, at 0-field, the flow in the hierarchical Andrei model is relevant, whereas it is marginal in the hierarchical $s-d$ model, which shows that the relevant direction carries little to no physical significance.\par
+\indent We will show that in the hierarchical $s-d$ model, the computation of the susceptibility reduces to iterating an {\it explicit} map relating 6 {\it running coupling constants} (rccs), and that this map can be obtained by restricting the flow equation for the hierarchical Andrei model [\cite{BGJ15}] to one of its invariant manifolds. The physics of both models are therefore very closely related, as had already been argued in [\cite{BGJ15}]. This is particularly noteworthy since, at 0-field, the flow in the hierarchical Andrei model is relevant, whereas it is marginal in the hierarchical $s-d$ model, which shows that the relevant direction carries little to no physical significance.\par
 \bigskip
 
-\indent The $s-d$ model [\cite{konSF}] represents a chain of non-interacting spin-1/2 fermions, called {\it electrons}, which interact with an isolated spin-1/2 {\it impurity} located at site 0. The Hilbert space of the system is $\mathcal F_L\otimes\mathbb C^2$ in which $\mathcal F_L$ is the Fock space of a length-$L$ chain of spin-1/2 fermions (the electrons) and $\mathbb C^2$ is the state space for the two-level impurity. The Hamiltonian, in the presence of a magnetic field of amplitude $h$ in the direction $\bm\omega\equiv(\bm\omega_1,\bm\omega_2,\bm\omega_3)$, is
+\indent The $s-d$ model [\cite{Ko64}] represents a chain of non-interacting spin-1/2 fermions, called {\it electrons}, which interact with an isolated spin-1/2 {\it impurity} located at site 0. The Hilbert space of the system is $\mathcal F_L\otimes\mathbb C^2$ in which $\mathcal F_L$ is the Fock space of a length-$L$ chain of spin-1/2 fermions (the electrons) and $\mathbb C^2$ is the state space for the two-level impurity. The Hamiltonian, in the presence of a magnetic field of amplitude $h$ in the direction $\bm\omega\equiv(\bm\omega_1,\bm\omega_2,\bm\omega_3)$, is
 \begin{equation}\begin{array}{r@{\ }>{\displaystyle}l}
 H_K=&H_0+V_0+V_h=:H_0+V\\[0.3cm]
 H_0=&\sum_{\alpha\in\{\uparrow,\downarrow\}}\sum_{x=-{L}/2}^{{L}/2-1} c^+_\alpha(x)\,\left(-\frac{\Delta}2-1\right)\,c^-_\alpha(x)\\[0.5cm]
@@ -48,7 +48,7 @@ V_h=&-h \,\sum_{j=1,2,3}\bm\omega_j \tau^j
 \end{array}\label{eqhamdef}\end{equation} 
 where $\lambda_0$ is the interaction strength, $\Delta$ is the discrete Laplacian $c_\alpha^\pm(x),\,\alpha=\uparrow,\downarrow$ are creation and annihilation operators acting on {\it electrons}, and $\sigma^j=\tau^j,\,j=1,2,3$, are Pauli matrices. The operators $\tau^j$ act on the {\it impurity}. The boundary conditions are taken to be periodic.\par
 
-\indent In the {\it Andrei model} [\cite{andEZ}], the impurity is represented by a fermion instead of a two-level system, that is the Hilbert space is replaced by $\mathcal F_L\otimes\mathcal F_1$, and the Hamiltonian is defined by replacing $\tau^j$ in~(\ref{eqhamdef}) by $d^+\tau^jd^-$ in which $d_\alpha^\pm(x),\,\alpha=\uparrow,\downarrow$ are creation and annihilation operators acting on the impurity.\par
+\indent In the {\it Andrei model} [\cite{An80}], the impurity is represented by a fermion instead of a two-level system, that is the Hilbert space is replaced by $\mathcal F_L\otimes\mathcal F_1$, and the Hamiltonian is defined by replacing $\tau^j$ in~(\ref{eqhamdef}) by $d^+\tau^jd^-$ in which $d_\alpha^\pm(x),\,\alpha=\uparrow,\downarrow$ are creation and annihilation operators acting on the impurity.\par
 \bigskip
 
 \indent The partition function $Z={\rm Tr}\, e^{-\beta H_K}$ can be expressed formally as a functional integral:
@@ -62,7 +62,7 @@ $$
 and the trace is over the state-space of the spin-1/2 impurity, that is a trace over $\mathbb C^2$.\par
 \bigskip
 
-\indent We will consider a {\it hierarchical} version of the $s-d$ model. The hierarchical model defined below is {\it inspired} by the $s-d$ model in the same way as the hierarchical model defined in [\cite{bgjOFi}] was inspired by the Andrei model. We will not give any details on the justification of the definition, as such considerations are entirely analogous to the discussion in [\cite{bgjOFi}].\par
+\indent We will consider a {\it hierarchical} version of the $s-d$ model. The hierarchical model defined below is {\it inspired} by the $s-d$ model in the same way as the hierarchical model defined in [\cite{BGJ15}] was inspired by the Andrei model. We will not give any details on the justification of the definition, as such considerations are entirely analogous to the discussion in [\cite{BGJ15}].\par
 
 \indent The model is defined by introducing a family of {\it hierarchical fields} and specifying a {\it propagator} for each pair of fields. The average of any monomial of fields is then computed using the Wick rule.\par
 
@@ -112,10 +112,10 @@ and find that
 with 
 \begin{equation}\begin{array}{r@{\quad}l}
 O_{0,\eta}^{[\le 0]}(\Delta):=\frac12\mathbf A^{[\le 0]}_\eta(\Delta)\cdot\bm\tau,& O_{1,\eta}^{[\le 0]}(\Delta):=\frac12\mathbf A^{[\le 0]}_\eta(\Delta)^2,\\[0.3cm]
-O_{4,\eta}^{[\le 0]}(\Delta):=\frac12\mathbf A^{[\le 0]}_\eta(\Delta)\cdot\bm\omega,& O_{5,\eta}^{[\le 0]}(\Delta):=\frac12\mathbf \bm\tau\cdot\bm\omega,\\[0.3cm]
+O_{4,\eta}^{[\le 0]}(\Delta):=\frac12\mathbf A^{[\le 0]}_\eta(\Delta)\cdot\bm\omega,& O_{5,\eta}^{[\le 0]}(\Delta):=\frac12 \bm\tau\cdot\bm\omega,\\[0.3cm]
 O_{6,\eta}^{[\le 0]}(\Delta):=\frac12(\mathbf A^{[\le 0]}_\eta(\Delta)\cdot\bm\omega)(\bm\tau\cdot\bm\omega),& O_{7,\eta}^{[\le 0]}(\Delta):=\frac12(\mathbf A^{[\le 0]}_\eta(\Delta)^2)(\bm\tau\cdot\bm\omega)
 \end{array}\label{eqOdef}\end{equation} 
-(the numbering is meant to recall that in [\cite{bgjOFi}]) in which $\bm\tau=(\tau^1,\tau^2,\tau^3)$ and $\mathbf A_\eta^{[\le 0]}(\Delta)$ is a vector of polynomials in the fields whose $j$-th component for $j\in\{1,2,3\}$ is 
+(the numbering is meant to recall that in [\cite{BGJ15}]) in which $\bm\tau=(\tau^1,\tau^2,\tau^3)$ and $\mathbf A_\eta^{[\le 0]}(\Delta)$ is a vector of polynomials in the fields whose $j$-th component for $j\in\{1,2,3\}$ is 
 \begin{equation}
 A_\eta^{[\le 0]j}(\Delta):=\sum_{(\alpha,\alpha')\in\{\uparrow,\downarrow\}^2} \psi_\alpha^{[\le 0]+}(\Delta_\eta)\sigma^j_{\alpha,\alpha'}\psi_{\alpha'}^{[\le 0]-}(\Delta_\eta)
 \label{eqAdef}\end{equation} 
@@ -123,7 +123,7 @@ $\psi_\alpha^{[\le 0]\pm}:=\sum_{m\le0}2^{\frac m2}\psi_\alpha^{[m]\pm}$, and
 \begin{equation}\begin{array}{r@{\ }>{\displaystyle}l}
 C=&\cosh(\tilde h),\quad \ell_0^{[0]}=\frac1C\frac{\lambda_0}{\tilde h}\sinh(\tilde h),\quad
 \ell_1^{[0]}=\frac1C\frac{\lambda_0^2}{12\tilde h}(\tilde h\cosh(\tilde h)+2\sinh(\tilde h))\\[0.3cm]
-\ell_4^{[0]}=&\frac1C\lambda_0\sinh(\tilde h),\quad \ell_5^{[0]}=\frac1C\sinh(\tilde h),\quad
+\ell_4^{[0]}=&\frac1C\lambda_0\sinh(\tilde h),\quad \ell_5^{[0]}=\frac2C\sinh(\tilde h),\quad
 \ell_6^{[0]}=\frac1C\frac{\lambda_0}{\tilde h}(\tilde h\cosh(\tilde h)-\sinh(\tilde h))\\[0.3cm]
 \ell_7^{[0]}=&\frac1C\frac{\lambda_0^2}{12\tilde h^2}(\tilde h^2\sinh(\tilde h)+2\tilde h\cosh(\tilde h)-2\sinh(\tilde h))
 \end{array}\label{eqinitcd}\end{equation} 
@@ -141,7 +141,7 @@ in terms of which
 \begin{equation}
 Z=C^{2|\mathcal Q_0|}\prod_{m=-N(\beta)+1}^0(C^{[m]})^{|\mathcal Q_{m-1}|}
 \label{eqZind}\end{equation} 
-in which $|\mathcal Q_m|=2^{N(\beta)-|m|}$ is the cardinality of $\mathcal Q_m$. In addition, similarly to [\cite{bgjOFi}], the map relating $\ell_p^{[m]}$ to $\ell_p^{[m-1]}$ and $C^{[m]}$ can be computed explicitly from~(\ref{eqindW}):
+in which $|\mathcal Q_m|=2^{N(\beta)-|m|}$ is the cardinality of $\mathcal Q_m$. In addition, similarly to [\cite{BGJ15}], the map relating $\ell_p^{[m]}$ to $\ell_p^{[m-1]}$ and $C^{[m]}$ can be computed explicitly from~(\ref{eqindW}):
 \begin{equation}\begin{array}{r@{\ }>{\displaystyle}l}
 C^{[m]} =& 1 +\frac{3}{2}\ell_{0}^2 +\ell_{0}\ell_{6} +9\ell_{1}^2 +\frac{\ell_{4}^2}{2} +\frac{\ell_{5}^2}{4} +\frac{\ell_{6}^2}{2} +9\ell_{7}^2 \\[0.3cm]
 \ell^{[m-1]}_{0} =& \frac1C\left(\ell_{0} -\ell_{0}^2 +3\ell_{0}\ell_{1} -\ell_{0}\ell_{6} \right)\\[0.3cm]
@@ -155,9 +155,9 @@ in which the $^{[m]}$ have been dropped from the right hand side.\par
 \bigskip
 
 
-\indent The flow equation~(\ref{eqbetafun}) can be recovered from that of the hierarchical Andrei model studied in [\cite{bgjOFi}] (see in particular [\cite{bgjOFi}, (C1)] by restricting the flow to the invariant submanifold defined by \begin{equation} \ell_2^{[m]}=\frac13,\quad \ell_3^{[m]}=\frac16\ell_1^{[m]},\quad \ell_8^{[m]}=\frac16\ell_4^{[m]}. \label{e18}\end{equation} This is of particular interest since $\ell_2^{[m]}$ is a relevant coupling and the fact that it plays no role in the $s-d$ model indicates that it has little to no physical relevance.\par
+\indent The flow equation~(\ref{eqbetafun}) can be recovered from that of the hierarchical Andrei model studied in [\cite{BGJ15}] (see in particular [\cite{BGJ15}, (C1)] by restricting the flow to the invariant submanifold defined by \begin{equation} \ell_2^{[m]}=\frac13,\quad \ell_3^{[m]}=\frac16\ell_1^{[m]},\quad \ell_8^{[m]}=\frac16\ell_4^{[m]}. \label{e18}\end{equation} This is of particular interest since $\ell_2^{[m]}$ is a relevant coupling and the fact that it plays no role in the $s-d$ model indicates that it has little to no physical relevance.\par
 
-\indent The qualitative behavior of the flow is therefore the same as that described in [\cite{bgjOFi}] for the hierarchical Andrei model. In particular the susceptibility, which can be computed by deriving $-\beta^{-1}\log Z$ with respect to $h$, remains finite in the 0-temperature limit as long as $\lambda_0<0$, that is as long as the interaction is anti-ferromagnetic.\par
+\indent The qualitative behavior of the flow is therefore the same as that described in [\cite{BGJ15}] for the hierarchical Andrei model. In particular the susceptibility, which can be computed by deriving $-\beta^{-1}\log Z$ with respect to $h$, remains finite in the 0-temperature limit as long as $\lambda_0<0$, that is as long as the interaction is anti-ferromagnetic.\par
 \hugeskip
 
 {\bf Acknowledgements}: We are grateful to G.~Benfatto for many enlightening discussions on the $s-d$ and Andrei's models.

bibliography.BBlog.tex

@@ -1,20 +1,4 @@
-\hrefanchor
-\outdef{citeandSO}{And61}
-\hbox{\parbox[t]{\rw}{[\cite{andSO}]}\parbox[t]{\colw}{P.~Anderson - {\it Localized magnetic states in metals}, Physical Review, Vol.~124, n.~1, p.~41-53, 1961.}}\par
-\bigskip
-
-\hrefanchor
-\outdef{citeandEZ}{And80}
-\hbox{\parbox[t]{\rw}{[\cite{andEZ}]}\parbox[t]{\colw}{N.~Andrei - {\it Diagonalization of the Kondo Hamiltonian}, Physical Review Letters, Vol.~45, n.~5, 1980.}}\par
-\bigskip
-
-\hrefanchor
-\outdef{citebgjOFi}{BGJ15}
-\hbox{\parbox[t]{\rw}{[\cite{bgjOFi}]}\parbox[t]{\colw}{G.~Benfatto, G.~Gallavotti, I.~Jauslin - {\it Kondo effect in a Fermionic hierarchical model}, arXiv 1506.04381, 2015.}}\par
-\bigskip
-
-\hrefanchor
-\outdef{citekonSF}{Kon64}
-\hbox{\parbox[t]{\rw}{[\cite{konSF}]}\parbox[t]{\colw}{J.~Kondo - {\it Resistance minimum in dilute magnetic alloys}, Progress of Theoretical Physics, Vol.~32, n.~1, 1964.}}\par
-\bigskip
-
+\BBlogentry{An61}{An61}{P.W. Anderson - {\it Localized magnetic states in metals}, Physical Review, Vol.~124, n.~1, p.~41-53, 1961, doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.124.41}{10.1103/PhysRev.124.41}}.}
+\BBlogentry{An80}{An80}{N. Andrei - {\it Diagonalization of the Kondo Hamiltonian}, Physical Review Letters, Vol.~45, n.~5, 1980, doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevLett.45.379}{10.1103/PhysRevLett.45.379}}.}
+\BBlogentry{BGJ15}{BGJ15}{G. Benfatto, G. Gallavotti, I. Jauslin - {\it Kondo effect in a Fermionic hierarchical model}, to appear in the Journal of Statistical Physics, 2015, doi:{\color{blue}\href{http://dx.doi.org/10.1007/s10955-015-1378-7}{10.1007/s10955-015-1378-7}}.}
+\BBlogentry{Ko64}{Ko64}{J. Kondo - {\it Resistance minimum in dilute magnetic alloys}, Progress of Theoretical Physics, Vol.~32, n.~1, 1964, doi:{\tt\color{blue}\href{http://dx.doi.org/10.1143/PTP.32.37}{10.1143/PTP.32.37}}.}

iansecs.sty

@@ -40,6 +40,16 @@
   \eject
 }
 
+%% prevent page breaks
+\newcount\prevpostdisplaypenalty
+\def\nopagebreakaftereq{
+  \prevpostdisplaypenalty=\postdisplaypenalty
+  \postdisplaypenalty=10000
+}
+\def\restorepagebreakaftereq{
+  \postdisplaypenalty=\prevpostdisplaypenalty
+}
+
 %% hyperlinks
 % hyperlinkcounter
 \newcounter{lncount}
@@ -64,15 +74,21 @@
 %% define a label for the latest tag
 %% label defines a command containing the string stored in \tag
 \AtBeginDocument{
-  \def\label#1{\expandafter\outdef{#1}{\safe\tag}}
+  \def\label#1{\expandafter\outdef{label@#1}{\safe\tag}}
+
+%% make a custom link at any given location in the document
+\def\makelink#1#2{
+  \hrefanchor
+  \outdef{label@#1}{#2}
+}
 
 \def\ref#1{%
 % check whether the label is defined (hyperlink runs into errors if this check is ommitted)
-\ifcsname #1@hl\endcsname%
-\hyperlink{ln.\csname #1@hl\endcsname}{\safe\csname #1\endcsname}%
+\ifcsname label@#1@hl\endcsname%
+\hyperlink{ln.\csname label@#1@hl\endcsname}{{\color{blue}\safe\csname label@#1\endcsname}}%
 \else%
-\ifcsname #1\endcsname%
-\csname #1\endcsname%
+\ifcsname label@#1\endcsname%
+{\color{blue}\csname #1\endcsname}%
 \else%
 {\bf ??}%
 \fi%
@@ -143,11 +159,9 @@
 \ifsubseqcount%
 \setcounter{seqcount}0%
 \fi%
-% space before subsection (if not first)
-\ifnum\thesubsectioncount>1%
+% space before subsection
 \subseqskip%
 \penalty-500%
-\fi%
 % hyperref anchor
 \hrefanchor
 % define tag (for \label)
@@ -180,11 +194,13 @@
 \newlength\itemizeseparator
 % space between the item symbol and the text
 \setlength\itemizeseparator{5pt}
+% penalty preceding an itemize
+\def\itemizepenalty{0}
 
 \newlength\current@itemizeskip
 \setlength\current@itemizeskip{0pt}
 \def\itemize{
-  \par\medskip
+  \par\penalty\itemizepenalty\medskip\penalty\itemizepenalty
   \addtolength\current@itemizeskip{\itemizeskip}
   \leftskip\current@itemizeskip
 }
@@ -202,6 +218,31 @@
   \hskip-\itempt@total\itemizept\hskip\itemizeseparator
 }
 
+%% enumerate
+\newcounter{enumerate@count}
+\def\enumerate{
+  \setcounter{enumerate@count}0
+  \let\olditem\item
+  \let\olditemizept\itemizept
+  \def\item{
+    % counter
+    \stepcounter{enumerate@count}
+    % set header
+    \def\itemizept{\theenumerate@count.}
+    % hyperref anchor
+    \hrefanchor
+    % define tag (for \label)
+    \xdef\tag{\theenumerate@count}
+    \olditem
+  }
+  \itemize
+}
+\def\endenumerate{
+  \enditemize
+  \let\item\olditem
+  \let\itemizept\olditemizept
+}
+
 %% points
 \def\point{
   \stepcounter{pointcount}
@@ -229,6 +270,17 @@
   % define tag (for \label)
   \xdef\tag{\thepointcount-\thesubpointcount-\thesubsubpointcount}
 }
+\def\pspoint{
+  \stepcounter{pointcount}
+  \stepcounter{subpointcount}
+  \setcounter{subsubpointcount}0
+  % hyperref anchor
+  \hrefanchor
+  \indent\hskip.5cm{\bf \thepointcount-\thesubpointcount\ - }
+  % define tag (for \label)
+  \xdef\tag{\thepointcount-\thesubpointcount}
+}
+  
 % reset points
 \def\resetpointcounter{
   \setcounter{pointcount}{0}
@@ -265,7 +317,7 @@
 \setlength\figwidth\textwidth
 \addtolength\figwidth{-2.5cm}
 
-\def\figcount#1{%
+\def\caption#1{%
 \stepcounter{figcount}%
 % hyperref anchor
 \hrefanchor%
@@ -279,7 +331,25 @@
 % define tag (for \label)
 \xdef\tag{\figformat}%
 % write
-\hfil fig \figformat: \parbox[t]{\figwidth}{\small#1}%
+\hfil fig \figformat: \parbox[t]{\figwidth}{\leavevmode\small#1}%
+\par\bigskip%
+}
+%% short caption: centered
+\def\captionshort#1{%
+\stepcounter{figcount}%
+% hyperref anchor
+\hrefanchor%
+% the number of the figure
+\edef\figformat{\thefigcount}%
+% add section number
+\ifsections%
+\let\tmp\figformat%
+\edef\figformat{\sectionprefix\thesectioncount.\tmp}%
+\fi%
+% define tag (for \label)
+\xdef\tag{\figformat}%
+% write
+\hfil fig \figformat: {\small#1}%
 \par\bigskip%
 }
 
@@ -290,10 +360,48 @@
 \def\endfigure{
   \par\penalty-1000
 }
-\let\caption\figcount
 
 %% delimiters
-\def\delimtitle#1{\par \leavevmode\raise.3em\hbox to\hsize{\lower0.3em\hbox{\vrule height0.3em}\hrulefill\ \lower.3em\hbox{#1}\ \hrulefill\lower0.3em\hbox{\vrule height0.3em}}\par\penalty10000}
+\def\delimtitle#1{\par%
+\leavevmode%
+\raise.3em\hbox to\hsize{%
+\lower0.3em\hbox{\vrule height0.3em}%
+\hrulefill%
+\ \lower.3em\hbox{#1}\ %
+\hrulefill%
+\lower0.3em\hbox{\vrule height0.3em}%
+}\par\penalty10000}
+
+%% callable by ref
+\def\delimtitleref#1{\par%
+% hyperref anchor
+\hrefanchor%
+% define tag (for \label)
+\xdef\tag{#1}%
+\leavevmode%
+\raise.3em\hbox to\hsize{%
+\lower0.3em\hbox{\vrule height0.3em}%
+\hrulefill%
+\ \lower.3em\hbox{\bf #1}\ %
+\hrulefill%
+\lower0.3em\hbox{\vrule height0.3em}%
+}\par\penalty10000}
+
+%% no title
+\def\delim{\par%
+\leavevmode\raise.3em\hbox to\hsize{%
+\lower0.3em\hbox{\vrule height0.3em}%
+\hrulefill%
+\lower0.3em\hbox{\vrule height0.3em}%
+}\par\penalty10000}
+
+%% end delim
+\def\enddelim{\par\penalty10000%
+\leavevmode%
+\raise.3em\hbox to\hsize{%
+\vrule height0.3em\hrulefill\vrule height0.3em%
+}\par}
+
 \def\delim{\par\leavevmode\raise.3em\hbox to\hsize{\vrule height0.3em\hrulefill\vrule height0.3em}\par\penalty10000}
 \def\enddelim{\par\penalty10000\leavevmode\raise.3em\hbox to\hsize{\vrule height0.3em\hrulefill\vrule height0.3em}\par}
 
@@ -317,6 +425,10 @@
   \delimtitle{\bf #1 \formattheo}
 }
 \let\endtheo\enddelim
+%% theorem headers with name
+\def\theoname#1#2{
+  \theo{#1}\hfil({\it #2})\par\penalty10000\medskip%
+}
 
 %% start appendices
 \def\appendix{%
@@ -381,12 +493,12 @@
   \stepcounter{tocsectioncount}
   \setcounter{tocsubsectioncount}{0}
   % write
-  \smallskip\hyperlink{ln.\csname toc@sec.\thetocsectioncount\endcsname}{{\bf \tocsectionprefix\thetocsectioncount}.\hskip5pt #1\leaderfill#2}\par
+  \smallskip\hyperlink{ln.\csname toc@sec.\thetocsectioncount\endcsname}{{\bf \tocsectionprefix\thetocsectioncount}.\hskip5pt {\color{blue}#1}\leaderfill#2}\par
 }
 \def\tocsubsection #1#2{
   \stepcounter{tocsubsectioncount}
   % write
-  {\hskip10pt\hyperlink{ln.\csname toc@subsec.\thetocsectioncount.\thetocsubsectioncount\endcsname}{{\bf \thetocsubsectioncount}.\hskip5pt {\small #1}\leaderfill#2}}\par
+  {\hskip10pt\hyperlink{ln.\csname toc@subsec.\thetocsectioncount.\thetocsubsectioncount\endcsname}{{\bf \thetocsubsectioncount}.\hskip5pt {\color{blue}\small #1}\leaderfill#2}}\par
 }
 \def\tocappendices{
   \medskip
@@ -397,6 +509,6 @@
 }
 \def\tocreferences#1{
   \medskip
-  {\hyperlink{ln.\csname toc@references\endcsname}{{\bf References}\leaderfill#1}}\par
+  {\hyperlink{ln.\csname toc@references\endcsname}{{\color{blue}\bf References}\leaderfill#1}}\par
   \smallskip
 }

toolbox.sty

@@ -34,8 +34,13 @@
   \@beginparpenalty=\prevparpenalty
 }
 
+%% stack relations in subscript or superscript
+\def\mAthop#1{\displaystyle\mathop{\scriptstyle #1}}
 
 %% array spanning the entire line
-\def\largearray{\begin{array}{@{}>{\displaystyle}l@{}}\hphantom{\hspace{\textwidth}}\\[-.5cm]}
+\newlength\largearray@width
+\setlength\largearray@width\textwidth
+\addtolength\largearray@width{-10pt}
+\def\largearray{\begin{array}{@{}>{\displaystyle}l@{}}\hphantom{\hspace{\largearray@width}}\\[-.5cm]}
 \def\endlargearray{\end{array}}