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Marginal Densities, Factor Graph Duality, and High-Temperature Series Expansions
[article]

2020
*
arXiv
*
pre-print

THE DUAL ISING MODEL AND

arXiv:1901.02733v3
fatcat:4lpt6pzlebcarbgewhvnwcge4q
*HIGH*-*TEMPERATURE**SERIES**EXPANSIONS*In [Jerrum and Sinclair, 1993] , the authors proposed a rapidly mixing Markov chain (called the subgraphsworld process) which evaluates the ... The configurations that arise in the*high*-*temperature**series**expansion*of the partition function (which are the configurations of the subgraphs-world process) coincide with the valid configurations in ...##
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High-temperature series expansions for random Potts models

2005
*
Condensed Matter Physics
*

We discuss recently generated

doi:10.5488/cmp.8.1.59
fatcat:gtqdqrynyvbwxoyld3s2yxgl7a
*high*-*temperature**series**expansions*for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. ... Using the star-graph*expansion*technique, quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension ... of the*high*-*temperature**series*. ...##
###
High-Temperature Series Expansions for Random Potts Models
[article]

2005
*
arXiv
*
pre-print

We discuss recently generated

arXiv:cond-mat/0502152v1
fatcat:jwmbrtg4nfh5dopbe5w44bcyzm
*high*-*temperature**series**expansions*for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. ... Using the star-graph*expansion*technique quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension ... of the*high*-*temperature**series*. ...##
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A New Method of the High Temperature Series Expansion
[article]

2002
*
arXiv
*
pre-print

We formulate a new method of performing

arXiv:cond-mat/0212123v1
fatcat:i3x5wrh3gvhp5kclfquhvxgzse
*high*-*temperature**series**expansions*for the spin-half Heisenberg model or, more generally, for SU(n) Heisenberg model with arbitrary n. ... These "quasi-moments" can be written in terms of corresponding "quasi-cumulants", which enable us to calculate higher-order terms in the*high*-*temperature**series**expansion*. ...*HIGH*-*TEMPERATURE**EXPANSION*In this section, we review*high*-*temperature**expansion*. Although the Heisenberg model is used for explanation, this review is more general. ...##
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High-temperature thermodynamics of the honeycomb-lattice Kitaev-Heisenberg model: A high-temperature series expansion study

2017
*
Physical review B
*

We develop

doi:10.1103/physrevb.96.144414
fatcat:zilhdzjd7vf57fdo2nyjyr44fy
*high**temperature**series**expansions*for the thermodynamic properties of the honeycomb-lattice Kitaev-Heisenberg model. ... These*expansions*show good convergence down to a*temperature*of a fraction of K and in some cases down to T=K/10. ... We develop*high**temperature**series**expansion*for the logarithm of the partition function using the linkedcluster method. ...##
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On equivalence of high temperature series expansion and coupling parameter series expansion in thermodynamic perturbation theory of fluids

2014
*
Journal of Chemical Physics
*

The coupling parameter

doi:10.1063/1.4871115
fatcat:vvypq43tuvafloj4bsmj4tqtny
*series**expansion*and the*high**temperature**series**expansion*in the ther- modynamic perturbation theory of fluids are shown to be equivalent if the interaction potential is pairwise ... As a consequence, for the class of fluids with the potential having a hardcore repulsion, if the hard-sphere fluid is chosen as reference system, the terms of coupling parameter*series**expansion*for radial ... The*series*is also known as*high**temperature**series**expansion*(HTSE). ...##
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High-temperature series expansion for spin-1/2 Heisenberg models

2017
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Computer Physics Communications
*

We present a

doi:10.1016/j.cpc.2016.09.003
fatcat:3k2zc7bqhzfg3kgq5flwou722e
*high*-*temperature**series**expansion*code for spin-1/2 Heisenberg models on arbitrary lattices. ... As an example we demonstrate how to use the application for an anisotropic triangular lattice with two independent couplings J1 and J2 and calculate the*high*-*temperature**series*of the magnetic susceptibility ...*High*-*temperature**Series**Expansions*The*high*-*temperature**series**expansions*(HTE) of a thermodynamic quantity Q in the inverse*temperature*β can be written as Q(β) = n a n β n . ...##
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High-temperature series expansions for random-bond Potts models on

2002
*
Computer Physics Communications
*

We use a star-graph

doi:10.1016/s0010-4655(02)00321-1
fatcat:7vtdckqmzzhrnpdxbyzz2ny23q
*expansion*technique to compute*high*-*temperature**series*for the free energy and susceptibility of randombond q-state Potts models on hypercubic lattices. ... For the bond-diluted Ising model (q = 2) in three dimensions we present first results for the critical*temperature*and exponent γ obtained from the analysis of susceptibility*series*up to order 19. ... Our*high*-*temperature**series**expansions*for the susceptibility up to order 19 are given with coefficients as polynomials in p, χ(v) = n a n (p)v n . ...##
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Specific heat of theS=12Heisenberg model on the kagome lattice: High-temperature series expansion analysis

2005
*
Physical Review B
*

We use a recently introduced technique to analyze

doi:10.1103/physrevb.71.014417
fatcat:2ds2y2vkhzabvcazfr23k7uis4
*high*-*temperature**series**expansion*based on the knowledge of*high*-*temperature**series**expansions*, the total entropy of the system and the low-*temperature*... In the case of kagome-lattice antiferromagnet, this method predicts a low-*temperature*peak at T/J<0.1. ... A hybrid method 21 based on exact diagonalizations and*high*-*temperature**series**expansion*gave a peak at T Ӎ 0.2 and c v Ӎ 0.17 for N =36 ͑see also Ref. 6͒. ...##
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High-temperature series expansions for theq-state Potts model on a hypercubic lattice and critical properties of percolation

2006
*
Physical Review E
*

We present results for the

doi:10.1103/physreve.74.051113
pmid:17279883
fatcat:xficbmmkvbhodkryyb4bplcjdm
*high*-*temperature**series**expansions*of the susceptibility and free energy of the q-state Potts model on a D-dimensional hypercubic lattice Z^D for arbitrary values of q. ... We also extend the 1/D*expansion*of the critical coupling for arbitrary values of q up to order D^-9. ... ACKNOWLEDGMENT The authors thank Joan Adler for discussions and help with the*series*analysis and Robert Ziff for a discussion on cluster cumulants. Support by DFG Grant No. ...##
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Finite and High-temperature series expansion via many-body perturbation theory
[article]

2021
*
arXiv
*
pre-print

We present a new algorithm to evaluate the grand potential at finite and

arXiv:2112.14311v1
fatcat:k5rdspga2nclpkpagzdxlom3lu
*high*-*temperature**series**expansion*via many-body perturbation theory. ... We obtain all coefficients of the*high*-*temperature**expansion*of the free energy and susceptibility per site of this model up to sixth order. ... We will show how this new reformulation helps us find the*high**temperatures**series**expansion*of the grand potential efficiently. ...##
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Random-bond Potts models on hypercubic lattices: high-temperature series expansions

2002
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Nuclear Physics B - Proceedings Supplements
*

We derive

doi:10.1016/s0920-5632(01)01887-4
fatcat:g3uky4frwnemxmuc6jqqawtt6u
*high*-*temperature**series**expansions*for the free energy and the susceptibility of random-bond qstate Potts models on hypercubic lattices using a stax-graph*expansion*technique. ... For the bond-diluted 4-state Potts model in three dimensions we present first results for the critical*temperature*as a function of p as obtained from the analysis of susceptibility*series*up to order ... Using*high*-*temperature**series**expansions*, on the other hand, one can obtain this average exactly. ...##
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Analysis of ising model critical exponents from high temperature series expansion

1979
*
Journal de Physique
*

Abstract. 2014

doi:10.1051/jphys:019790040010096900
fatcat:mheifbve6jek3htm4oilfi56ji
*High**temperature**series**expansion*for the critical exponents of the Ising model are reanalysed using a modified ratio method. ... 2014 Nous analysons les*séries*de haute*température*relatives aux exposants critiques du modèle d'Ising, à l'aide d'une méthode de rapports modifiée. ... Analysis of Ising model critical exponents from*high**temperature**series**expansion*J. ...##
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High-Temperature Series Expansions for a Spin-1 Model of Ferromagnetism

1973
*
Physical Review B
*

PHYSICAL REVIEW B
VOLUME 7, NUMBER 9

doi:10.1103/physrevb.7.4284
fatcat:u562ehwfazcojj4ndmk2573r6i
*High*-*Temperature**Series**Expansions*for a Spin-1 Mode1 of Ferromagnetism" H. H. ... These*temperatures*are obtained from*high*-*temperature**series**expansions*(HTS), the molecular-field approximation (MFA), and the constant-coupling approximation (CCA). ...##
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Logarithmic divergent specific heat from high-temperature series expansions: application to the two-dimensional XXZ Heisenberg model
[article]

2021
*
arXiv
*
pre-print

The method uses the fact that c_v is constrained both by its

arXiv:2108.03010v1
fatcat:hu772nqhb5g2thzoecmd23chr4
*high**temperature**series**expansion*, and just above T_c by the type of singularity. ... We present an interpolation method for the specific heat c_v(T), when there is a phase transition with a logarithmic singularity in c_v at a critical*temperature*T=T_c. ... Finally,*high*-*temperature**series**expansion*(HTSE) methods operate directly in the thermodynamic limit but cannot reach very low*temperatures*, a limitation which becomes more restrictive when there are ...
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