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

Mehdi Molkaraie
2020 arXiv   pre-print
THE DUAL ISING MODEL AND 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  ... 
arXiv:1901.02733v3 fatcat:4lpt6pzlebcarbgewhvnwcge4q

High-temperature series expansions for random Potts models

M. Hellmund, W. Janke
2005 Condensed Matter Physics  
We discuss recently generated 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.  ... 
doi:10.5488/cmp.8.1.59 fatcat:gtqdqrynyvbwxoyld3s2yxgl7a

High-Temperature Series Expansions for Random Potts Models [article]

Meik Hellmund, Wolfhard Janke
2005 arXiv   pre-print
We discuss recently generated 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.  ... 
arXiv:cond-mat/0502152v1 fatcat:jwmbrtg4nfh5dopbe5w44bcyzm

A New Method of the High Temperature Series Expansion [article]

Noboru Fukushima
2002 arXiv   pre-print
We formulate a new method of performing 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.  ... 
arXiv:cond-mat/0212123v1 fatcat:i3x5wrh3gvhp5kclfquhvxgzse

High-temperature thermodynamics of the honeycomb-lattice Kitaev-Heisenberg model: A high-temperature series expansion study

R. R. P. Singh, J. Oitmaa
2017 Physical review B  
We develop 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.  ... 
doi:10.1103/physrevb.96.144414 fatcat:zilhdzjd7vf57fdo2nyjyr44fy

On equivalence of high temperature series expansion and coupling parameter series expansion in thermodynamic perturbation theory of fluids

A. Sai Venkata Ramana
2014 Journal of Chemical Physics  
The coupling parameter 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).  ... 
doi:10.1063/1.4871115 fatcat:vvypq43tuvafloj4bsmj4tqtny

High-temperature series expansion for spin-1/2 Heisenberg models

Andreas Hehn, Natalija van Well, Matthias Troyer
2017 Computer Physics Communications  
We present a 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 .  ... 
doi:10.1016/j.cpc.2016.09.003 fatcat:3k2zc7bqhzfg3kgq5flwou722e

High-temperature series expansions for random-bond Potts models on

Meik Hellmund, Wolfhard Janke
2002 Computer Physics Communications  
We use a star-graph 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 .  ... 
doi:10.1016/s0010-4655(02)00321-1 fatcat:7vtdckqmzzhrnpdxbyzz2ny23q

Specific heat of theS=12Heisenberg model on the kagome lattice: High-temperature series expansion analysis

G. Misguich, B. Bernu
2005 Physical Review B  
We use a recently introduced technique to analyze 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.  ... 
doi:10.1103/physrevb.71.014417 fatcat:2ds2y2vkhzabvcazfr23k7uis4

High-temperature series expansions for theq-state Potts model on a hypercubic lattice and critical properties of percolation

Meik Hellmund, Wolfhard Janke
2006 Physical Review E  
We present results for the 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.  ... 
doi:10.1103/physreve.74.051113 pmid:17279883 fatcat:xficbmmkvbhodkryyb4bplcjdm

Finite and High-temperature series expansion via many-body perturbation theory [article]

Mohamed Amine Tag, Abid Boudiar, Mohamed El-Hadi Mansour, Abdelkader Hafdallah, Chafia Bendjeroudib
2021 arXiv   pre-print
We present a new algorithm to evaluate the grand potential at finite and 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.  ... 
arXiv:2112.14311v1 fatcat:k5rdspga2nclpkpagzdxlom3lu

Random-bond Potts models on hypercubic lattices: high-temperature series expansions

Meik Hellmund, Wolfhard Janke
2002 Nuclear Physics B - Proceedings Supplements  
We derive 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.  ... 
doi:10.1016/s0920-5632(01)01887-4 fatcat:g3uky4frwnemxmuc6jqqawtt6u

Analysis of ising model critical exponents from high temperature series expansion

J. Zinn-Justin
1979 Journal de Physique  
Abstract. 2014 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.  ... 
doi:10.1051/jphys:019790040010096900 fatcat:mheifbve6jek3htm4oilfi56ji

High-Temperature Series Expansions for a Spin-1 Model of Ferromagnetism

H. H. Chen, Peter M. Levy
1973 Physical Review B  
PHYSICAL REVIEW B VOLUME 7, NUMBER 9 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).  ... 
doi:10.1103/physrevb.7.4284 fatcat:u562ehwfazcojj4ndmk2573r6i

Logarithmic divergent specific heat from high-temperature series expansions: application to the two-dimensional XXZ Heisenberg model [article]

M. G. Gonzalez, B. Bernu, L. Pierre, L. Messio
2021 arXiv   pre-print
The method uses the fact that c_v is constrained both by its 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  ... 
arXiv:2108.03010v1 fatcat:hu772nqhb5g2thzoecmd23chr4
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