arXiv:1404.6564 · Journal of Physics A Mathematical and Theoretical

The dual model for an Ising model with nearest and next-nearest neighbors

Adam Strycharski, Zbigniew Koza

Published Jul 4, 2013• 3 citations

Abstract

We construct and analyze a dual model to the next-nearest-neighbor Ising (NNNI) model on the rectangular lattice. The Hamiltonian of the dual model turns out to contain two- and four-spin interactions. The free fermion approximation suggests that an increase in the critical temperature of the dual model caused by the four-spin interactions is limited to a finite range.

DOI: 10.1088/1751-8113/46/29/295003

Related papers

Phase diagram of the mixed spin Ising model with four-spin interaction and nextnearest neighbor couplings

Majid Mouhib, Mouhcine Azhari, Noureddine Benayad

The phase diagrams of the ferromagnetic two-dimensional mixed spin-1 and spin-1/2 Ising model with four-spin interaction J4 and next-nearest couplings J’ are investigated by the use of the finite cluster approximation based on single-site cluster theory. The state equations are derived for the two-dimensional square lattice. The phase diagram is qualitatively and quantitatively different from that obtained when the interaction J’ is ignored. In fact, the system exhibits a variety of interesting features resulting from the introduction of the next-nearest neighbor interaction (NNN). It undergoes two kinds of behavior according to the negative and the positive value of J’. In particular, for J4/J2=-4, the system keeps the coexistence of the two ground state up to J’-dependent finite temperature.

PRSMAug 7, 20151 citation

Phase transitions in the antiferromagnetic ising model on a square lattice with next-nearest-neighbor interactions

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, Felix A. Kassan-Ogly +1 more

The phase transitions in the two-dimensional Ising model on a square lattice are studied using a replica algorithm, the Monte Carlo method, and histogram analysis with allowance for the next-nearest-neighbor interactions in the range 0.1 ≤ r < 1.0. A phase diagram is constructed for the dependence of the critical temperature on the next-nearest-neighbor interaction. A second-order phase transition is detected in this range and the model under study.

Journal of Experimental and Theoretical PhysicsDec 1, 201328 citations

CRITICAL PROPERTY TO THE ISING MODEL WITH NEXT-NEAREST-NEIGHBOR INTERACTIONS ON A DECORATED SQUARE LATTICE

Sun Chun-Feng

Using the decimation technique,a square decorated Ising lattice with two kinds of interactionsK1andK2was transformed into a regular square Ising lattice with nearest-neighbor,next-nearest-neighbor,and four-spin interactions.The critical fixed point was found at K1C=0.5125,and K2C=0.2134,which determines the critical temperature of the system.The universality was discussed in this system.

Diwen wuli xuebaoJan 1, 20120 citations

Phase diagram and critical exponent ν for the nearest-neighbor and next-nearest-neighbor interaction Ising model

James L. Monroe, Seung‐Yeon Kim

We obtain an approximation of the phase diagram of an Ising model with both nearest-neighbor and next-nearest-neighbor interactions on the square lattice. We use the Fisher zeros of the partition functions of a sequence of finite-sized systems along with various extrapolation methods to obtain phase transition points. In addition, we obtain an approximate value of the correlation length critical exponent nu. Our results are compared to previous results for this system using a wide variety of other approaches.

Physical Review EAug 29, 200730 citations

Next-Nearest-Neighbor Ising Model

R. W. Gibberd

The next-nearest-neighbor two-dimensional Ising model is cast into a form which resembles a one-dimensional interacting many-fermion system. An approximation, which has previously been shown to be successful in giving the critical properties of the two-dimensional ferroelectric problem, is used. From the approximate expression obtained, the critical indices are found to be α = α′ = 0, β = ⅛, which agrees with the results obtained from series expansions and plausible physical arguments. The critical temperature obtained agrees to within 6% of the series expansion results.

Journal of Mathematical PhysicsJun 1, 196930 citations

Hamiltonian limit of the two-dimensional axial next-nearest-neighbor Ising model: A many-body approach

Santiago D’Elía

The Hamiltonian limit of the two-dimensional axial next-nearest-neighbor Ising model is studied with use of an interacting-fermion technique. Details of the ferromagnetic side of the corresponding phase diagram are analyzed, especially the characterization of spatially modulated structures and the type of the phase transition.

Physical review. B, Condensed matterAug 1, 19921 citation