Diagrammatical Techniques for Two-Dimensional Ising Models. III. Ising Model to Vertex 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.

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The Grassmann Representation of Ising Model

International Journal of Modern Physics B ◽

10.1142/s0217979298001162 ◽

1998 ◽

Vol 12 (20) ◽

pp. 1995-2003 ◽

Cited By ~ 7

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.

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

International Journal of Modern Physics B ◽

10.1142/s0217979288000056 ◽

1988 ◽

Vol 02 (01) ◽

pp. 49-63 ◽

Cited By ~ 13

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.

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DOMAIN GROWTH IN COMPRESSIBLE 2D ISING MODELS UNDERGOING PHASE SEPARATION

International Journal of Modern Physics C ◽

10.1142/s0129183109014394 ◽

2009 ◽

Vol 20 (09) ◽

pp. 1325-1333 ◽

Cited By ~ 2

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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MAPPING OF p-STATE SYMMETRIC VERTEX MODEL ON THE HONEYCOMB LATTICE ONTO ITS ISING-SPIN COUNTERPART

International Journal of Modern Physics B ◽

10.1142/s021797929200013x ◽

1992 ◽

Vol 06 (02) ◽

pp. 251-260 ◽

Cited By ~ 1

Author(s):

L. ŠAMAJ ◽

M. KOLESÍK

Keyword(s):

Ising Model ◽

Parameter Space ◽

Ising Models ◽

Honeycomb Lattice ◽

Model Parameters ◽

Vertex Model ◽

Free Energies ◽

Gauge Transformations ◽

Ising Spin ◽

Arbitrary Lattice

The mapping which produces a path between the p-state symmetric vertex model and the Ising model with spin [Formula: see text] on the honeycomb lattice is constructed. The mapping construction is based on a combination of decoration and gauge transformations. The formulation enables one to find the manifold in the vertex weights parameter space on which the mapping can be performed and to derive dual relations among the model parameters as well as the free energies of related symmetric vertex and Ising models. The extension of the mapping to arbitrary lattice coordination is outlined.

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

International Journal of Modern Physics B ◽

10.1142/s0217979202015819 ◽

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.

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