scholarly journals Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

2009 ◽  
Vol 137 (4) ◽  
pp. 667-699 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Robert Shrock
Keyword(s):  
Magnetic Field ◽  
Partition Function ◽  
Potts Model ◽  
Transfer Matrices

scholarly journals Spin models in complex magnetic fields: a hard sign problem

2018 ◽  
Vol 175 ◽  
pp. 07026 ◽  
Author(s):  
Philippe de Forcrand ◽  
Tobias Rindlisbacher
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Partition Function ◽  
External Field ◽  
Potts Model ◽  
Cluster Algorithm ◽  
Spin Models ◽  
Sign Problem ◽  
Special Cases ◽  
Severe Sign

Coupling spin models to complex external fields can give rise to interesting phenomena like zeroes of the partition function (Lee-Yang zeroes, edge singularities) or oscillating propagators. Unfortunately, it usually also leads to a severe sign problem that can be overcome only in special cases; if the partition function has zeroes, the sign problem is even representation-independent at these points. In this study, we couple the N-state Potts model in different ways to a complex external magnetic field and discuss the above mentioned phenomena and their relations based on analytic calculations (1D) and results obtained using a modified cluster algorithm (general D) that in many cases either cures or at least drastically reduces the sign-problem induced by the complex external field.

FORMAL CONSTRAINTS ON SERIES ANALYSIS ON THE POTTS MODEL

1987 ◽  
Vol 01 (04) ◽  
pp. 145-153 ◽  
Author(s):  
D. HANSEL ◽  
J.M. MAILLARD
Keyword(s):  
Magnetic Field ◽  
Partition Function ◽  
Low Temperature ◽  
Potts Model ◽  
Correlation Functions ◽  
Exact Results ◽  
Nearest Neighbour ◽  
Temperature Expansion ◽  
Higher Dimensional ◽  
Formal Constraints

It is shown that the low temperature expansion of the partition function, magnetization and nearest neighbour correlation functions of the q-state checkerboard Potts model in a magnetic field drastically simplify on a very simple algebraic variety. These four formal constraints on the expansions are also analysed in the framework of the resummed low temperature expansions and the large q expansions. These exact results are generalized straightforwardly to higher dimensional hypercubic lattices and also to some random problems.

scholarly journals Parallel family trees for transfer matrices in the Potts model

2015 ◽  
Vol 187 ◽  
pp. 55-71 ◽  
Author(s):  
Cristobal A. Navarro ◽  
Fabrizio Canfora ◽  
Nancy Hitschfeld ◽  
Gonzalo Navarro
Keyword(s):  
Potts Model ◽  
Transfer Matrices ◽  
Family Trees

scholarly journals Zeros of the Potts model partition function on Sierpinski graphs

2013 ◽  
Vol 377 (9) ◽  
pp. 671-675 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Robert Shrock
Keyword(s):  
Partition Function ◽  
Potts Model ◽  
Sierpiński Graphs
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