Ising model on the Bethe lattice with competing interactions up to the third-nearest-neighbor generation

We consider a general spin-1/2 Ising model with multisite interaction on the Husimi lattice with the coordination number q and derive an analytical expression of correlation functions for stable fixed points of the corresponding recurrence relation. We show that for q=2 our model transforms to the two-state vertex model on the Bethe lattice with q=3 and for the case q=3, with only nearest neighbor interactions, we transform our model to the corresponding model on the Bethe lattice with q=3, using the Yang–Baxter equations.

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Field behavior of an Ising model with competing interactions on the Bethe lattice

Physical Review E ◽

10.1103/physreve.52.2187 ◽

1995 ◽

Vol 52 (3) ◽

pp. 2187-2197 ◽

Cited By ~ 29

Author(s):

Marcelo H. R. Tragtenberg ◽

Carlos S. O. Yokoi

Keyword(s):

Ising Model ◽

Bethe Lattice ◽

Competing Interactions ◽

Field Behavior

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Ising Model on the Bethe Lattice with Competing Interactions

Journal of the Physical Society of Japan ◽

10.1143/jpsj.44.1768 ◽

1978 ◽

Vol 44 (6) ◽

pp. 1768-1773 ◽

Cited By ~ 3

Author(s):

Shunichi Muto ◽

Takehiko Oguchi

Keyword(s):

Ising Model ◽

Bethe Lattice ◽

Competing Interactions

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SHORT-TIME DYNAMIC EXPONENTS OF AN ISING MODEL WITH COMPETING INTERACTIONS

Modern Physics Letters B ◽

10.1142/s0217984903005068 ◽

2003 ◽

Vol 17 (05n06) ◽

pp. 209-218 ◽

Cited By ~ 6

Author(s):

NELSON ALVES ◽

JOSÉ ROBERTO DRUGOWICH DE FELÍCIO

Keyword(s):

Ising Model ◽

Critical Exponents ◽

Order Parameter ◽

Nearest Neighbor ◽

Time Correlation ◽

Time Behavior ◽

Two Dimensional ◽

Competing Interactions ◽

Time Dynamic ◽

Short Time

In this work the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions is revisited. We obtain the dynamic critical exponents z and θ from short-time Monte Carlo simulations. The dynamic critical exponent z is obtained from the time behavior of the ratio [Formula: see text], whereas the non-universal exponent θ is estimated from the time correlation of the order parameter <M(0)M(t)> ~ tθ, where M(t) is the order parameter at instant t, d is the dimension of the system and <(⋯)> is the average of the quantity (⋯) over different samples. We also obtain the static critical exponents β and ν by investigating the time behavior of the magnetization.

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The Ising model with nearest- and next-nearest-neighbor interactions on the Bethe lattice: The exact recursion relations

Modern Physics Letters B ◽

10.1142/s0217984920500876 ◽

2020 ◽

Vol 34 (10) ◽

pp. 2050087

Author(s):

Erhan Albayrak

Keyword(s):

Phase Transition ◽

Ising Model ◽

Nearest Neighbor ◽

Bethe Lattice ◽

Model Parameters ◽

Thermal Variation ◽

Recursion Relations ◽

Coordination Numbers ◽

First Order ◽

Special Points

The Ising model with nearest- and next-nearest-neighbor (NNN) bilinear interactions is examined on the Bethe lattice (BL) in terms of exact recursion relations (ERR) when the external magnetic [Formula: see text] is turned on. The thermal variation of the magnetization belonging to the central spin is investigated to calculate the possible phase diagrams of the model for given coordination numbers. Different phase regions, ferromagnetic (FM), antiferromagnetic (AFM) and paramagnetic (PM), are discovered and the phase lines in terms of first-order or second-order phase transitions are calculated. These lines are found to be order–disorder or order–order phase transition lines. It is also found that they combine at some special points or terminate at some end points for appropriate values of the model parameters.

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