The Grassmann Representation of Ising Model

1998 ◽  
Vol 12 (20) ◽  
pp. 1995-2003 ◽  
Author(s):  
K. Nojima
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Ising Models ◽  
Integral Representations ◽  
Dimensional Case ◽  
Partition Functions ◽  
Fermion Field ◽  
Two Dimensional

The integral representations for the partition functions of Ising models are surveyed. The connection with the underlying fermion field in the two-dimensional case is discussed. The relation between the low and the high-temperature expansions is examined.

HIGH-TEMPERATURE SUSCEPTIBILITY SERIES FOR SQUARE-LATTICE ISING MODEL WITH FIRST AND SECOND NEIGHBOUR INTERACTIONS

2002 ◽  
Vol 16 (32) ◽  
pp. 4919-4922
Author(s):  
KEH YING LIN ◽  
MALL CHEN
Keyword(s):  
High Temperature ◽  
Critical Temperature ◽  
Ising Model ◽  
Critical Exponent ◽  
Ising Models ◽  
Temperature Series ◽  
Square Lattice ◽  
Zero Field ◽  
Two Dimensional ◽  
Temperature Susceptibility

We have calculated the high-temperature series expansion of the zero-field susceptibility of the square-lattice Ising model with first and second neighbour interactions to the 20th order by computer. Our results extend the previous calculation by Hsiao and Lin to two more orders. We use the Padé approximants to estimate the critical exponent γ and the critical temperature. Our result 1.747 < γ < 1.753 supports the universality conjecture that all two-dimensional Ising models have the same critical exponent γ = 1.75.

Local three-spin correlations in the free-fermion and planar Ising models

1989 ◽  
Vol 423 (1865) ◽  
pp. 279-300 ◽  
Keyword(s):  
Ising Model ◽  
Ising Models ◽  
Square Lattice ◽  
Free Fermion ◽  
Two Dimensional ◽  
Solvable Models ◽  
Spin Correlations ◽  
Fermion Model ◽  
Free Fermion Model

A number of local three-spin correlations are calculated exactly for various related ferromagnetic two-dimensional solvable models in statistical mechanics.They are the square lattice free-fermion model, the equivalent checkerboard Ising model, and the anisotropic triangular, honeycomb and square lattice Ising models. The different results are all applications of a single unifying formula.

ISING MODELS ON TWO-DIMENSIONAL QUASI-CRYSTALS: SOME EXACT RESULTS

1988 ◽  
Vol 02 (01) ◽  
pp. 49-63 ◽  
Author(s):  
T. C. CHOY
Keyword(s):  
Ising Model ◽  
Critical Exponents ◽  
Ising Models ◽  
Critical Surface ◽  
Exact Results ◽  
Two Dimensional ◽  
Soluble Model ◽  
De Bruijn ◽  
Quasi Crystals ◽  
Conventional Picture

Exactly soluble Z-invariant (or Baxter) models of statistical mechanics are generalised on two-dimensional Penrose lattices based on the de Bruijn construction. A unique soluble model is obtained for each realization of the Penrose lattice. Analysis of these models shows that they are soluble along a line in parameter space which intersects the critical surface at a point that can be determined exactly. In the Ising case, critical exponents along this line are identical with the regular two-dimensional Ising model thus supporting the conventional picture of the universality hypothesis.

Inference for general Ising models

1982 ◽  
Vol 19 (A) ◽  
pp. 345-357 ◽  
Author(s):  
David K. Pickard
Keyword(s):  
Ising Model ◽  
Thermodynamic Parameters ◽  
Limit Theorems ◽  
Ising Models ◽  
Confidence Regions ◽  
Likelihood Inference ◽  
Partition Functions ◽  
Polynomial Equations ◽  
Interaction Energies ◽  
Asymptotic Inference

In previous papers (1976), (1977a), (1979) limit theorems were obtained for the classical Ising model, and these provided the basis for asymptotic inference. The present paper extends these results to more general Ising models. In two and more dimensions, likelihood inference for the thermodynamic parameters (i.e. the interaction energies) is effectively impossible. The problem is that the error in locating critical and/or confidence regions is as large as their diameters. To remedy this requires more accurate characterizations of the partition functions, but these seem unlikely to be forthcoming. Besag's coding estimators for these parameters are inverse hyperbolic tangents of the roots of simultaneous polynomial equations and hence avoid such location errors. However, little is yet known about their sampling characteristics. Finally, likelihood inference for lattice averages (an alternative parametrization) is straightforward from the limit theorems.

DOMAIN GROWTH IN COMPRESSIBLE 2D ISING MODELS UNDERGOING PHASE SEPARATION

2009 ◽  
Vol 20 (09) ◽  
pp. 1325-1333 ◽  
Author(s):  
S. J. MITCHELL ◽  
D. P. LANDAU
Keyword(s):  
Monte Carlo ◽  
Phase Separation ◽  
Ising Model ◽  
Time Domain ◽  
Spin Exchange ◽  
Ising Models ◽  
Domain Growth ◽  
Late Time ◽  
Two Dimensional ◽  
Continuous Particle

High precision Monte Carlo simulations are used to study domain growth in a compressible two-dimensional spin-exchange Ising model with continuous particle positions and zero total magnetization. For mismatched systems, we measure significant deviations from the theoretically expected late-time domain growth, R(t) = A + Btn with n = 1/3. For a compressible model with no mismatch, we measure only a slight deviation from n = 1/3. Our results indicate that our current understanding of domain growth is incomplete.

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