scholarly journals A New Look at the 2D Ising Model from Exact Partition Function Zeros for Large Lattice Sizes

1997 ◽  
Vol 08 (05) ◽  
pp. 1063-1071 ◽  
Author(s):  
Nelson A. Alves ◽  
J. R. Drugowich de Felicio ◽  
Ulrich H. E. Hansmann
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Numerical Method ◽  
Square Lattice ◽  
Corrections To Scaling ◽  
Partition Function Zeros ◽  
Alternative Method ◽  
Large Lattice ◽  
Function Zeros ◽  
New Look

A general numerical method is presented to locate the partition function zeros in the complex β plane for large lattice sizes. We apply this method to the 2D Ising model and results are reported for square lattice sizes up to L = 64. We also propose an alternative method to evaluate corrections to scaling which relies only on the leading zeros. This method is illustrated with our data.

scholarly journals PARTITION FUNCTION ZEROS OF A RESTRICTED POTTS MODEL ON SELF-DUAL STRIPS OF THE SQUARE LATTICE

2007 ◽  
Vol 21 (10) ◽  
pp. 1755-1773 ◽  
Author(s):  
SHU-CHIUAN CHANG ◽  
ROBERT SHROCK
Keyword(s):  
Partition Function ◽  
Potts Model ◽  
Square Lattice ◽  
Partition Function Zeros ◽  
Large Width ◽  
Function Zeros ◽  
Continuous Accumulation

We calculate the partition function Z(G, Q, v) of the Q-state Potts model exactly for self-dual cyclic square-lattice strips of various widths Ly and arbitrarily large lengths Lx, with Q and v restricted to satisfy the relation Q=v2. From these calculations, in the limit Lx→∞, we determine the continuous accumulation locus [Formula: see text] of the partition function zeros in the v and Q planes. A number of interesting features of this locus are discussed and a conjecture is given for properties applicable to arbitrarily large width. Relations with the loci [Formula: see text] for general Q and v are analyzed.

scholarly journals YANG–LEE AND FISHER ZEROS GENERALIZED ON SOME FAR-FROM-EQUILIBRIUM SYSTEMS

2009 ◽  
Vol 23 (03) ◽  
pp. 375-381
Author(s):  
K. G. SARGSYAN
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Minimal Models ◽  
Partition Function Zeros ◽  
Nontrivial Behavior ◽  
Far From Equilibrium ◽  
Fisher Zeros ◽  
Function Zeros ◽  
Simple Models

A generalization of the Yang–Lee and Fisher zeros on far-from-equilibrium systems coupled with two thermal baths is proposed. The Yang–Lee zeros were obtained for minimal models which exhibit complicated behavior in the context of the partition function zeros and provide an analitycal treatment. This type of model may be considered as a simplest one and analogous to Ising model for equilibrium. The obtained distributions of generalized Yang–Lee zeros show nontrivial behavior for these simple models.

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