Series expansions from corner transfer matrices: The square lattice Ising model

1979 ◽  
Vol 21 (2) ◽  
pp. 103-123 ◽  
Author(s):  
R. J. Baxter ◽  
I. G. Enting
Keyword(s):  
Ising Model ◽  
Square Lattice ◽  
Series Expansions ◽  
Transfer Matrices ◽  
Corner Transfer Matrices

CONFORMAL PROPERTIES OF CRITICAL ISING MODEL CORNER TRANSFER MATRICES

1990 ◽  
Vol 04 (05) ◽  
pp. 907-912
Author(s):  
Brian DAVIES ◽  
Paul A. PEARCE
Keyword(s):  
Ising Model ◽  
Central Charge ◽  
Finite Size ◽  
Summation Formula ◽  
Transfer Matrices ◽  
Corner Transfer Matrices ◽  
Free Boundary Conditions ◽  
Large N ◽  
Fermion Algebra ◽  
Virasoro Characters

The scaling spectra of finite-size Ising model corner transfer matrices (CTMs) are studied at criticality, using the fermion algebra. The low-lying eigenvalues collapse like 1/ log N for large N as predicted by conformal invariance. The shift in the largest eigenvalue is evaluated analytically using a generalized Euler-Maclaurin summation formula giving πc/6 log N with central charge c=1/2. The spectrum generating functions, for both fixed and free boundary conditions, are expressed simply in terms of the c=1/2 Virasoro characters χ∆(q) with modular parameter q= exp (−π/ log N) and conformal dimensions ∆=0, 1/2, 1/16.

LOW-TEMPERATURE SERIES EXPANSIONS FOR SQUARE-LATTICE ISING MODEL WITH FIRST AND SECOND NEIGHBOUR INTERACTIONS

2002 ◽  
Vol 16 (32) ◽  
pp. 4911-4917
Author(s):  
YEE MOU KAO ◽  
MALL CHEN ◽  
KEH YING LIN
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Low Temperature ◽  
Spontaneous Magnetization ◽  
Temperature Series ◽  
Square Lattice ◽  
Series Expansions ◽  
Zero Field ◽  
Ferromagnetic Ising Model ◽  
Neighbour Interaction

We have calculated the low-temperature series expansions of the spontaneous magnetization and the zero-field susceptibility of the square-lattice ferromagnetic Ising model with first-neighbour interaction J1 and second-neighbour interaction J2 to the 30th and 26th order respectively by computer. Our results extend the previous calculations by Lee and Lin to six more orders. We use the Padé approximants to estimate the critical exponents and the critical temperature for different ratios of R = J2/J1. The estimated critical temperature as a function of R agrees with the estimation by Oitmaa from high-temperature series expansions.

SERIES EXPANSIONS FOR THE ISING MODEL COUPLED TO TWO HEAT BATHS

1995 ◽  
Vol 09 (24) ◽  
pp. 3181-3188 ◽  
Author(s):  
A. V. BAKAEV ◽  
V. I. KABANOVICH
Keyword(s):  
Ising Model ◽  
Square Lattice ◽  
Series Expansions ◽  
Temperature Ratio ◽  
Spin Models ◽  
High Temperature Expansion ◽  
Different Temperatures ◽  
Lattice Spin Models ◽  
Good Agreement ◽  
Non Equilibrium

We present an algorithm for generating high- and low-temperature expansions for non-equilibrium steady states in lattice spin models coupled to two thermal baths at different temperatures. For the Ising model on a square lattice with the sublattice temperature ratio α = Ta/Tb we construct the high-temperature expansion of energy to order eleven. The estimates of T c are in good agreement with the exact equilibrium result (at α = 1) and the existing Monte-Carlo simulations in non equilibrium cases (α = 2 and α = ∞).

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