% Crystallization @article{Mainini2014, title={Crystallization in carbon nanostructures}, author={Mainini, Edoardo and Stefanelli, Ulisse}, journal={Communications in Mathematical Physics}, volume={328}, pages={545--571}, year={2014}, publisher={Springer} } @article{Theil2006, title={A proof of crystallization in two dimensions}, author={Theil, Florian}, journal={Communications in Mathematical Physics}, volume={262}, pages={209--236}, year={2006}, publisher={Springer} } @article{Jansen2014, title={Wigner crystallization in the quantum 1D jellium at all densities}, author={Jansen, Sabine and Jung, Paul}, journal={Communications in Mathematical Physics}, volume={331}, pages={1133--1154}, year={2014}, publisher={Springer} } % Insight into continuous systems @article{Ruelle1971, title={Existence of a phase transition in a continuous classical system}, author={Ruelle, David}, journal={Physical Review Letters}, volume={27}, number={16}, pages={1040}, year={1971}, publisher={APS} } % Mermin-Wagner @article{Mermin1966, title={Absence of ferromagnetism or antiferromagnetism in one-or two-dimensional isotropic Heisenberg models}, author={Mermin, N David and Wagner, Herbert}, journal={Physical Review Letters}, volume={17}, number={22}, pages={1133}, year={1966}, publisher={APS} } % J-L @article{Jauslin2017, title={Crystalline ordering and large fugacity expansion for hard-core lattice particles}, author={Jauslin, Ian and Lebowitz, Joel L}, journal={The Journal of Physical Chemistry B}, volume={122}, number={13}, pages={3266--3271}, year={2017}, publisher={ACS Publications} } @article{Jauslin2018, title={High-Fugacity Expansion, Lee--Yang Zeros, and Order--Disorder Transitions in Hard-Core Lattice Systems}, author={Jauslin, Ian and Lebowitz, Joel L}, journal={Communications in Mathematical Physics}, volume={364}, pages={655--682}, year={2018}, publisher={Springer} } % Series by Mazel et al @article{Mazel2018, title={High-density hard-core model on triangular and hexagonal lattices}, author={Mazel, A and Stuhl, I and Suhov, Y}, journal={arXiv preprint arXiv:1803.04041}, year={2018} } @article{Mazel2019, title={High-density hard-core model on $\mathbb{Z}^2$ and norm equations in ring $\mathbb{Z}[\sqrt[6]{-1}]$}, author={Mazel, A and Stuhl, I and Suhov, Y}, journal={arXiv preprint arXiv:1909.11648}, year={2019} } @article{Mazel2020, title={The hard-core model on planar lattices: the disk-packing problem and high-density Gibbs distributions}, author={Mazel, A and Stuhl, I and Suhov, Y}, journal={arXiv preprint arXiv:2011.14156}, year={2020} } @article{Mazel2021, title={Kepler's conjecture and phase transitions in the high-density hard-core model on $\mathbb{Z}^3$}, author={Mazel, A and Stuhl, I and Suhov, Y}, journal={arXiv preprint arXiv:2112.14250}, year={2021} } % Voronoi diagram for graphs @article{Mehlhorn1988, title={A faster approximation algorithm for the Steiner problem in graphs}, author={Mehlhorn, Kurt}, journal={Information Processing Letters}, volume={27}, number={3}, pages={125--128}, year={1988}, publisher={Elsevier} } @article{Erwig2000, title={The graph Voronoi diagram with applications}, author={Erwig, Martin}, journal={Networks: An International Journal}, volume={36}, number={3}, pages={156--163}, year={2000}, publisher={Wiley Online Library} } % Voronoi dual on graphs @article{Honiden2010, title={Approximate shortest path queries using Voronoi duals}, author={Honiden, Shinichi and Houle, Michael E and Sommer, Christian and Wolff, Martin}, journal={Transactions on computational science IX: special issue on Voronoi diagrams in science and engineering}, pages={28--53}, year={2010}, publisher={Springer} } % Pirogov-Sinai theory @article{Pirogov1975, title={Phase diagrams of classical lattice systems}, author={Pirogov, SA and Sinai, Ya G}, journal={Theoretical and Mathematical Physics}, volume={25}, number={3}, pages={1185--1192}, year={1975} } @article{Zahradnk1984, title={An alternate version of Pirogov-Sinai theory}, author={Milo{\v s} Zahradn{\'i}k}, journal={Communications in Mathematical Physics}, year={1984}, volume={93}, pages={559-581} } @article{Borgs1989, title={A unified approach to phase diagrams in field theory and statistical mechanics}, author={Borgs, Christian and Imbrie, John Z}, journal={Communications in mathematical physics}, volume={123}, number={2}, pages={305--328}, year={1989}, publisher={Springer} } @book{Presutti2008, title={Scaling limits in statistical mechanics and microstructures in continuum mechanics}, author={Presutti, Errico}, year={2008}, publisher={Springer Science \& Business Media} } % m-potential @article{Holsztynski1978, title={Peierls condition and number of ground states}, author={Holsztynski, W and Slawny, J}, journal={Communications in Mathematical Physics}, volume={61}, pages={177--190}, year={1978}, publisher={Springer} } % Cluster expansion @book{Friedli2017, title={Statistical mechanics of lattice systems: a concrete mathematical introduction}, author={Friedli, Sacha and Velenik, Yvan}, year={2017}, publisher={Cambridge University Press} } @article{Ueltschi2003, author = {Ueltschi, Daniel}, year = {2003}, month = {05}, pages = {}, title = {Cluster Expansions and Correlation Functions}, volume = {4}, journal = {Moscow Mathematical Journal}, doi = {10.17323/1609-4514-2004-4-2-511-522} } % GFc's @article{Timar2013, title={Boundary-connectivity via graph theory}, author={Tim{\'a}r, {\'A}d{\'a}m}, journal={Proceedings of the American Mathematical Society}, volume={141}, number={2}, pages={475--480}, year={2013} } @article{Gaunt1965, title={Hard-sphere lattice gases. I. Plane-square lattice}, author={Gaunt, David S and Fisher, Michael E}, journal={The Journal of Chemical Physics}, volume={43}, number={8}, pages={2840--2863}, year={1965}, publisher={American Institute of Physics} } % Sphere packing @article{Hales2005, title={A proof of the Kepler conjecture}, author={Hales, Thomas C}, journal={Annals of mathematics}, pages={1065--1185}, year={2005}, publisher={JSTOR} } @article{Hales2010, title={The dodecahedral conjecture}, author={Hales, Thomas and McLaughlin, Sean}, journal={Journal of the American Mathematical Society}, volume={23}, number={2}, pages={299--344}, year={2010} } @article{Berryman1983, title={Random close packing of hard spheres and disks}, author={Berryman, James G}, journal={Physical Review A}, volume={27}, number={2}, pages={1053}, year={1983}, publisher={APS} } @article{Adams1972, title={Computation of dense random packings of hard spheres}, author={Adams, DJ and Matheson, AJ}, journal={The Journal of Chemical Physics}, volume={56}, number={5}, pages={1989--1994}, year={1972}, publisher={American Institute of Physics} } @article{Viazovska2017, title={The sphere packing problem in dimension 8}, author={Viazovska, Maryna S}, journal={Annals of Mathematics}, pages={991--1015}, year={2017}, publisher={JSTOR} } @article{Cohn2017, title={The sphere packing problem in dimension 24}, author={Cohn, Henry and Kumar, Abhinav and Miller, Stephen and Radchenko, Danylo and Viazovska, Maryna}, journal={Annals of Mathematics}, volume={185}, number={3}, pages={1017--1033}, year={2017}, publisher={Department of Mathematics, Princeton University Princeton, New Jersey, USA} } @article{Isobe2015, title={Hard-sphere melting and crystallization with event-chain Monte Carlo}, author={Isobe, Masaharu and Krauth, Werner}, journal={The Journal of chemical physics}, volume={143}, number={8}, pages={084509}, year={2015}, publisher={AIP Publishing LLC} } % Sliding @article{Hadas2022, title={Columnar order in random packings of $2\times 2$ squares on the square lattice}, author={Hadas, Daniel and Peled, Ron}, journal={arXiv preprint arXiv:2206.01276}, year={2022} } % Physics @article{WJ57, doi = {10.1063/1.1743956}, url = {https://doi.org/10.1063%2F1.1743956}, year = 1957, month = {nov},publisher = {{AIP} Publishing}, volume = {27}, number = {5}, pages = {1207--1208}, author = {W. W. Wood and J. D. Jacobson}, title = {Preliminary Results from a Recalculation of the Monte Carlo Equation of State of Hard Spheres}, journal = {The Journal of Chemical Physics} } @article{AW57, doi = {10.1063/1.1743957}, url = {https://doi.org/10.1063%2F1.1743957}, year = 1957, month = {nov},publisher = {{AIP} Publishing}, volume = {27}, number = {5}, pages = {1208--1209}, author = {B. J. Alder and T. E. Wainwright}, title = {Phase Transition for a Hard Sphere System}, journal = {The Journal of Chemical Physics} } @article{PM86, doi = {10.1038/320340a0}, url = {https://doi.org/10.1038%2F320340a0}, year = 1986, month = {mar},publisher = {Springer Nature}, volume = {320}, number = {6060}, pages = {340--342}, author = {P. N. Pusey and W. van Megen}, title = {Phase behaviour of concentrated suspensions of nearly hard colloidal spheres}, journal = {Nature} } @article{St88, doi = {10.1103/revmodphys.60.161}, url = {https://doi.org/10.1103%2Frevmodphys.60.161}, year = 1988, month = {jan}, publisher = {American Physical Society ({APS})}, volume = {60}, number = {1}, pages = {161--207}, author = {Katherine J. Strandburg}, title = {Two-dimensional melting}, journal = {Reviews of Modern Physics} } @book{Mc10, title={Advanced statistical mechanics}, author={McCoy, Barry M}, series={International Series of Monographs on Physics}, volume={146}, year={2010}, publisher={Oxford University Press}} @article{BK11, doi = {10.1103/physrevlett.107.155704}, url = {https://doi.org/10.1103%2Fphysrevlett.107.155704}, year = 2011, month = {oct}, publisher = {American Physical Society ({APS})}, volume = {107}, number = {15},author = {Etienne P. Bernard and Werner Krauth}, title = {Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition}, journal = {Physical Review Letters} , pages={155704}} % High fugacity expansions @article{Do68, doi = {10.1007/bf01075682}, url = {https://doi.org/10.1007%2Fbf01075682}, year = 1969, publisher = {Springer Nature}, volume = {2}, number = {4}, pages = {302--312}, author = {R. L. Dobrushin}, title = {The problem of uniqueness of a gibbsian random field and the problem of phase transitions}, journal = {Functional Analysis and Its Applications} } @article{HP74, doi = {10.1088/0305-4470/7/15/017}, url = {https://doi.org/10.1088%2F0305-4470%2F7%2F15%2F017}, year = 1974, month = {oct}, publisher = {{IOP} Publishing}, volume = {7}, number = {15}, pages = {1913--1917}, author = {O J Heilmann and E Praestgaard}, title = {Phase transition in a lattice gas with third nearest neighbour exclusion on a square lattice}, journal = {Journal of Physics A: Mathematical, Nuclear and General} } @article{EB05, doi = {10.1209/epl/i2005-10166-3}, url = {https://doi.org/10.1209%2Fepl%2Fi2005-10166-3}, year = 2005, month = {sep}, publisher = {{IOP} Publishing}, volume = {71}, number = {6}, pages = {900--905}, author = {E Eisenberg and A Baram}, title = {A first-order phase transition and a super-cooled fluid in a two-dimensional lattice gas model}, journal = {Europhysics Letters ({EPL})} } % Exactly solvable @book{Ba82, title={Exactly solved models in statistical mechanics}, author={Baxter, Rodney J}, year={1982}, publisher={Academic Press}} % Lee-Yang @article{YL52, doi = {10.1103/physrev.87.404}, url = {https://doi.org/10.1103%2Fphysrev.87.404}, year = 1952, month = {aug}, publisher = {American Physical Society ({APS})}, volume = {87}, number = {3}, pages = {404--409}, author = {C. N. Yang and T. D. Lee}, title = {Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation}, journal = {Physical Review} } @article{LY52, doi = {10.1103/physrev.87.410}, url = {https://doi.org/10.1103%2Fphysrev.87.410}, year = 1952, month = {aug}, publisher = {American Physical Society ({APS})}, volume = {87}, number = {3}, pages = {410--419}, author = {T. D. Lee and C. N. Yang}, title = {Statistical Theory of Equations of State and Phase Transitions. {II}. Lattice Gas and Ising Model}, journal = {Physical Review} } % Mayer expansion @article{Ma37, doi = {10.1063/1.1749933}, url = {https://doi.org/10.1063%2F1.1749933}, year = 1937, month = {jan},publisher = {{AIP} Publishing}, volume = {5}, number = {1}, pages = {67--73}, author = {Joseph E. Mayer}, title = {The Statistical Mechanics of Condensing Systems. I}, journal = {The Journal of Chemical Physics} } @article{Ur27, doi = {10.1017/s0305004100011191}, url = {https://doi.org/10.1017%2Fs0305004100011191}, year = 1927, month = {apr}, publisher = {Cambridge University Press ({CUP})}, volume = {23}, number = {06}, pages = {685}, author = {H. D. Ursell}, title = {The evaluation of Gibbs{\textquotesingle} phase-integral for imperfect gases}, journal = {Mathematical Proceedings of the Cambridge Philosophical Society} } @article{Ru63, doi = {10.1016/0003-4916(63)90336-1}, url = {https://doi.org/10.1016%2F0003-4916%2863%2990336-1}, year = 1963, month = {oct}, publisher = {Elsevier {BV}}, volume = {25}, number = {1}, pages = {109--120}, author = {David Ruelle}, title = {Correlation functions of classical gases}, journal = {Annals of Physics} } % Textbook @book{FV17, doi = {10.1017/9781316882603}, url = {https://doi.org/10.1017%2F9781316882603}, year = 2017, month = {nov}, publisher = {Cambridge University Press}, author = {Sacha Friedli and Yvan Velenik}, title = {Statistical Mechanics of Lattice Systems} }