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

  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},
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… 
Three-dimensional Ising model with nearest- and next-nearest-neighbor interactions.
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
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
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
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
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
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
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.
  • Y. Nishiyama
  • Physics, Medicine
    Physical 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
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
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


The magnetization of the 3D Ising model
We present highly accurate Monte Carlo results for simple cubic Ising lattices containing up to spins. These results were obtained by means of the Cluster Processor, a newly built special-purpose
Gonihedric 3D Ising actions
Abstract We investigate a generalized Ising action containing nearest neighbour, next to nearest neighbour and plaquette terms that has been suggested as a potential string worldsheet discretization
Phase transition in lattice surface systems with gonihedric action
Abstract We prove the existence of an ordered low-temperature phase in a model of soft-self-avoiding closed random surfaces on a cubic lattice by a suitable extension of Peierls contour method. The
Exactly solved models in statistical mechanics
exactly solved models in statistical mechanics exactly solved models in statistical mechanics rodney j baxter exactly solved models in statistical mechanics exactly solved models in statistical