Cluster expansion and spectrum of the transfer matrix of the two-dimensional ising model with strong external field

1984 ◽  
Vol 60 (1) ◽  
pp. 734-735
Author(s):  
P. V. Khrapov
Keyword(s):  
Ising Model ◽  
External Field ◽  
Transfer Matrix ◽  
Cluster Expansion ◽  
Two Dimensional ◽  
Strong External Field

Transfer Matrix of the Two-dimensional Ising Model

2020 ◽  
pp. 211-234
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Ising Model ◽  
Critical Point ◽  
Transfer Matrix ◽  
Functional Equations ◽  
Baxter Equation ◽  
Matrix Formalism ◽  
Two Dimensional ◽  
R Matrix ◽  
Transfer Matrix Formalism ◽  
Lowest Eigenvalue

This chapter deals with the exact solution of the two-dimensional Ising model as it is achieved through the transfer matrix formalism. It discusses the crucial role played by the commutative properties of the transfer matrices, which lead to a functional equation for their eigenvalues. The exact free energy of the Ising model and its critical point can be identified by means of the lowest eigenvalue. The chapter covers Baxter's approach, the Yang–Baxter equation and its relation to the Boltzmann weights, the R-matrix, and discusses activity away from the critical point, the six-vertex model, as well as functional equations and symmetries.

TWO-DIMENSIONAL WANG–LANDAU SAMPLING OF AN ASYMMETRIC ISING MODEL

2009 ◽  
Vol 20 (09) ◽  
pp. 1357-1366 ◽  
Author(s):  
SHAN-HO TSAI ◽  
FUGAO WANG ◽  
D. P. LANDAU
Keyword(s):  
Phase Diagram ◽  
Ising Model ◽  
External Field ◽  
Density Of States ◽  
Triangular Lattice ◽  
Sampling Method ◽  
Two Dimensional ◽  
Theoretical Predictions ◽  
The Spectator ◽  
Three Body

We study the critical endpoint behavior of an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. We use a two-dimensional Wang–Landau sampling method to determine the density of states for this model. An accurate density of states allowed us to map out the phase diagram accurately and observe a clear divergence of the curvature of the spectator phase boundary and of the derivative of the magnetization coexistence diameter near the critical endpoint, in agreement with previous theoretical predictions.

A-B droplets for a two-dimensional antiferromagnetic Ising model in external field H

1983 ◽  
Vol 16 (16) ◽  
pp. 3925-3930 ◽  
Author(s):  
C Amitrano ◽  
F di Liberto ◽  
R Figari ◽  
F Peruggi
Keyword(s):  
Ising Model ◽  
External Field ◽  
Two Dimensional ◽  
Antiferromagnetic Ising Model
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