Dimer piling problems and interacting field theory

Ramirez Camasca, Rolando; McGreevy, John

doi:10.1103/PhysRevD.110.065017

Title: Dimer piling problems and interacting field theory

Journal Article · 23 September 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.110.065017 · OSTI ID:2447516

;

The dimer tiling problem asks in how many ways can the edges of a graph be covered by dimers so that each site is covered once. In the special case of a planar graph, this problem has a solution in terms of a free fermionic field theory. We rediscover and explore an expression for the number of coverings of an arbitrary graph by arbitrary objects in terms of an interacting fermionic field theory first proposed by Samuel. Generalizations of the dimer tiling problem, which we call “dimer piling problems,” demand that each site be covered $N$ times by indistinguishable dimers. Our field theory provides a solution of these problems in the large- $N$ limit. We give a similar path integral representation for certain lattice coloring problems. Published by the American Physical Society 2024

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009919

OSTI ID:: 2447516

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 6 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (40)

Logarithmic correction to BPS black hole entropy from supersymmetric index at finite temperature Anupam, A. H.; Athira, P. V.; Chowdhury, Chandramouli Journal of High Energy Physics, Vol. 2024, Issue 3 https://doi.org/10.1007/JHEP03(2024)095	journal	March 2024
Logarithmic corrections to Schwarzschild and other non-extremal black hole entropy in different dimensions Sen, Ashoke Journal of High Energy Physics, Vol. 2013, Issue 4 https://doi.org/10.1007/JHEP04(2013)156	journal	April 2013
Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates Sen, Ashoke General Relativity and Gravitation, Vol. 44, Issue 5 https://doi.org/10.1007/s10714-012-1336-5	journal	February 2012
The statistics of dimers on a lattice Kasteleyn, P. W. Physica, Vol. 27, Issue 12 https://doi.org/10.1016/0031-8914(61)90063-5	journal	December 1961
Feynman diagrams for the Yang-Mills field Faddeev, L. D.; Popov, V. N. Physics Letters B, Vol. 25, Issue 1 https://doi.org/10.1016/0370-2693(67)90067-6	journal	July 1967
A planar diagram theory for strong interactions Hooft, G. 't Nuclear Physics B, Vol. 72, Issue 3 https://doi.org/10.1016/0550-3213(74)90154-0	journal	April 1974
Kac-Moody symmetries of critical ground states Kondev, Jané; Henley, Christopher L. Nuclear Physics B, Vol. 464, Issue 3 https://doi.org/10.1016/0550-3213(96)00064-8	journal	April 1996
From quantum mechanics to classical statistical physics: Generalized Rokhsar–Kivelson Hamiltonians and the “Stochastic Matrix Form” decomposition Castelnovo, Claudio; Chamon, Claudio; Mudry, Christopher Annals of Physics, Vol. 318, Issue 2 https://doi.org/10.1016/j.aop.2005.01.006	journal	August 2005
Colorings of a Hexagonal Lattice Baxter, R. J. Journal of Mathematical Physics, Vol. 11, Issue 3 https://doi.org/10.1063/1.1665210	journal	March 1970
Dimer Statistics and Phase Transitions Kasteleyn, P. W. Journal of Mathematical Physics, Vol. 4, Issue 2 https://doi.org/10.1063/1.1703953	journal	February 1963
The use of anticommuting variable integrals in statistical mechanics. I. The computation of partition functions Samuel, Stuart Journal of Mathematical Physics, Vol. 21, Issue 12 https://doi.org/10.1063/1.524404	journal	December 1980
The use of anticommuting variable integrals in statistical mechanics. II. The computation of correlation functions Samuel, Stuart Journal of Mathematical Physics, Vol. 21, Issue 12 https://doi.org/10.1063/1.524405	journal	December 1980
The use of anticommuting variable integrals in statistical mechanics. III. Unsolved models Samuel, Stuart Journal of Mathematical Physics, Vol. 21, Issue 12 https://doi.org/10.1063/1.524406	journal	December 1980
Conway's Tiling Groups Thurston, William P. The American Mathematical Monthly, Vol. 97, Issue 8 https://doi.org/10.1080/00029890.1990.11995660	journal	October 1990
Dimer problem in statistical mechanics-an exact result Temperley, H. N. V.; Fisher, Michael E. Philosophical Magazine, Vol. 6, Issue 68 https://doi.org/10.1080/14786436108243366	journal	August 1961
Operator spectrum and exact exponents of the fully packed loop model Kondev, Jané; Gier, Jan de; Nienhuis, Bernard Journal of Physics A: Mathematical and General, Vol. 29, Issue 20 https://doi.org/10.1088/0305-4470/29/20/007	journal	October 1996
Statistical Mechanics of Dimers on a Plane Lattice Fisher, Michael E. Physical Review, Vol. 124, Issue 6 https://doi.org/10.1103/PhysRev.124.1664	journal	December 1961
Statistical Mechanics of Dimers on a Plane Lattice. II. Dimer Correlations and Monomers Fisher, Michael E.; Stephenson, John Physical Review, Vol. 132, Issue 4 https://doi.org/10.1103/PhysRev.132.1411	journal	November 1963
Residual Entropy of Square Ice Lieb, Elliott H. Physical Review, Vol. 162, Issue 1 https://doi.org/10.1103/PhysRev.162.162	journal	October 1967
Classical antiferromagnets on the Kagomé lattice Huse, David A.; Rutenberg, Andrew D. Physical Review B, Vol. 45, Issue 13 https://doi.org/10.1103/PhysRevB.45.7536	journal	April 1992
Kagome ´ spin-1/2 antiferromagnets in the hyperbolic plane Elser, Veit; Zeng, Chen Physical Review B, Vol. 48, Issue 18 https://doi.org/10.1103/PhysRevB.48.13647	journal	November 1993
Classical dimers on the triangular lattice Fendley, P.; Moessner, R.; Sondhi, S. L. Physical Review B, Vol. 66, Issue 21 https://doi.org/10.1103/PhysRevB.66.214513	journal	December 2002
Dynamical obstruction in a constrained system and its realization in lattices of superconducting devices Castelnovo, Claudio; Pujol, Pierre; Chamon, Claudio Physical Review B, Vol. 69, Issue 10 https://doi.org/10.1103/PhysRevB.69.104529	journal	March 2004
Generalized Elitzur’s theorem and dimensional reductions Batista, C. D.; Nussinov, Zohar Physical Review B, Vol. 72, Issue 4 https://doi.org/10.1103/PhysRevB.72.045137	journal	July 2005
Quantum three-coloring dimer model and the disruptive effect of quantum glassiness on its line of critical points Castelnovo, Claudio; Chamon, Claudio; Mudry, Christopher Physical Review B, Vol. 72, Issue 10 https://doi.org/10.1103/PhysRevB.72.104405	journal	September 2005
Weakly coupled non-Abelian anyons in three dimensions Freedman, Michael; Hastings, Matthew B.; Nayak, Chetan Physical Review B, Vol. 84, Issue 24 https://doi.org/10.1103/PhysRevB.84.245119	journal	December 2011
Heisenberg-Kitaev model on the hyperhoneycomb lattice Lee, Eric Kin-Ho; Schaffer, Robert; Bhattacharjee, Subhro Physical Review B, Vol. 89, Issue 4 https://doi.org/10.1103/PhysRevB.89.045117	journal	January 2014
Three-dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite- D approximation Kimchi, Itamar; Analytis, James G.; Vishwanath, Ashvin Physical Review B, Vol. 90, Issue 20 https://doi.org/10.1103/PhysRevB.90.205126	journal	November 2014
Colorings of odd or even chirality on hexagonal lattices Cépas, O. Physical Review B, Vol. 95, Issue 6 https://doi.org/10.1103/PhysRevB.95.064405	journal	February 2017
Dynamical symmetry breaking in asymptotically free field theories Gross, David J.; Neveu, André Physical Review D, Vol. 10, Issue 10 https://doi.org/10.1103/PhysRevD.10.3235	journal	November 1974
Impossibility of spontaneously breaking local symmetries Elitzur, S. Physical Review D, Vol. 12, Issue 12 https://doi.org/10.1103/PhysRevD.12.3978	journal	December 1975
Random trimer tilings Ghosh, Anandamohan; Dhar, Deepak; Jacobsen, Jesper L. Physical Review E, Vol. 75, Issue 1 https://doi.org/10.1103/PhysRevE.75.011115	journal	January 2007
Critical Exponents for Charged and Neutral Bose Gases aboveλPoints Ma, Shang-keng Physical Review Letters, Vol. 29, Issue 19 https://doi.org/10.1103/PhysRevLett.29.1311	journal	November 1972
Superconductivity and the Quantum Hard-Core Dimer Gas Rokhsar, Daniel S.; Kivelson, Steven A. Physical Review Letters, Vol. 61, Issue 20 https://doi.org/10.1103/PhysRevLett.61.2376	journal	November 1988
Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model Moessner, R.; Sondhi, S. L. Physical Review Letters, Vol. 86, Issue 9 https://doi.org/10.1103/PhysRevLett.86.1881	journal	February 2001
Quantum Dimer Model on the Kagome Lattice: Solvable Dimer-Liquid and Ising Gauge Theory Misguich, G.; Serban, D.; Pasquier, V. Physical Review Letters, Vol. 89, Issue 13 https://doi.org/10.1103/PhysRevLett.89.137202	journal	September 2002
Entropy and chirality in sphinx tilings Huber, Greg; Knecht, Craig; Trump, Walter Physical Review Research, Vol. 6, Issue 1 https://doi.org/10.1103/PhysRevResearch.6.013227	journal	March 2024
Doping a Mott insulator: Physics of high-temperature superconductivity Lee, Patrick A.; Nagaosa, Naoto; Wen, Xiao-Gang Reviews of Modern Physics, Vol. 78, Issue 1 https://doi.org/10.1103/RevModPhys.78.17	journal	January 2006
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries Jerrum, Mark; Sinclair, Alistair; Vigoda, Eric Journal of the ACM, Vol. 51, Issue 4 https://doi.org/10.1145/1008731.1008738	journal	July 2004
Theory of Superconductivity Schrieffer, J. R. CRC Press https://doi.org/10.1201/9780429495700	book	March 2018

Similar Records

ALP contribution to the strong

C P

problem

Journal Article · 2024 · Physical Review. D. · OSTI ID:2474214

Enguita, V.; Gavela, B.; Grinstein, B.; +1 more

Sokolov-Ternov effect in rotating systems

Journal Article · 2025 · Physical Review. D. · OSTI ID:2528117

Kroth, Jonathan D.; Tuchin, Kirill

Antipodal self-duality of square fishnet graphs

Journal Article · 2025 · Physical Review. D. · OSTI ID:2565750

Dixon, Lance J.; Duhr, Claude

Title: Dimer piling problems and interacting field theory

Citation Formats

References (40)

Similar Records

Related Subjects