# Critical behavior of the three-dimensional Ising model with nearest-neighbor, next-nearest-neighbor, and plaquette interactions

@article{Cirillo1997CriticalBO, title={Critical behavior of the three-dimensional Ising model with nearest-neighbor, next-nearest-neighbor, and plaquette interactions}, author={Emilio N. M. Cirillo and Giuseppe Gonnella and Alessandro Pelizzola}, journal={Physical Review E}, year={1997}, volume={55} }

The critical and multicritical behavior of the simple cubic Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions is studied using the cube and star-cube approximations of the cluster variation method and the recently proposed cluster variation--Pad\'e approximant method. Particular attention is paid to the line of critical end points of the ferromagnetic-paramagnetic phase transition: its (multi)critical exponents are calculated, and their values suggest that the…

## 20 Citations

Three-dimensional Ising model with nearest- and next-nearest-neighbor interactions.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

The phase diagram of the Ising model in the presence of nearest- and next-nearest-neighbor interactions on a simple cubic lattice is studied within the framework of the differential operator…

QUALITATIVE ASPECTS OF THE PHASE DIAGRAM OF J1–J2 MODEL ON THE CUBIC LATTICE

- Physics
- 2013

The qualitative aspects of the phase diagram of the Ising model on the cubic lattice, with ferromagnetic (F) nearest-neighbor interactions (J1) and antiferromagnetic (AF) next-nearest-neighbor…

Plaquette Ising models, degeneracy and scaling

- Physics
- 2017

Abstract
We review some recent investigations of the 3d plaquette Ising model. This displays a strong first-order phase transition with unusual scaling properties due to the size-dependent degeneracy…

Dynamics of the Ising Chain with Four-Spin Interactions in a Disordered Transverse Magnetic Field

- Physics
- 2001

We study the time dependent behavior of the four-spin interactions Ising chain in the presence of a disordered transverse magnetic field. In order to analyze the effects of field randomness in the…

Investigation of probability theory on Ising models with different four-spin interactions

- Mathematics
- 2017

Based on probability theory, two types of three-dimensional Ising models with different four-spin interactions are studied. Firstly the partition function of the system is calculated by considering…

The dual gonihedric 3D Ising model

- Physics
- 2011

We investigate the dual of the κ = 0 gonihedric Ising model on a 3D cubic lattice, which may be written as an anisotropically coupled Ashkin–Teller model. The original κ = 0 gonihedric model has a…

The Gonihedric Ising Model and Glassiness

- Physics, Mathematics
- 2007

The Gonihedric 3D Ising model is a lattice spin model in which planar Peierls boundaries between + and - spins can be created at zero energy cost. Instead of weighting the area of Peierls boundaries…

Multicriticality of the (2+1) -dimensional gonihedric model: a realization of the (d,m)=(3,2) Lifshitz point.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

Multicriticality of the gonihedric model in 2+1 dimensions is investigated numerically and the criticality in terms of the crossover (multicritical) scaling theory is analyzed.

String tension in gonihedric three-dimensional Ising models

- Mathematics, Physics
- 1997

For the 3D gonihedric Ising models defined by Savvidy and Wegner the bare string tension is zero and the energy of a spin interface depends only on the number of bends and self-intersections, in…

Finite size analysis of the 3D gonihedric Ising model with k=0

- Physics
- 1998

We perform a high statistics analysis of the phase transition for the 3D Gonihedric Ising model with κ = 0. This corresponds to an enhanced symmetry point in a class of models defined by Savvidy and…

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