# Phase Diagram and Critical Exponents of the ±J Ising Model in Finite Dimensions by Monte Carlo Renormalization Group

@article{Ozeki1987PhaseDA,
title={Phase Diagram and Critical Exponents of the ±J Ising Model in Finite Dimensions by Monte Carlo Renormalization Group},
author={Yukiyasu Ozeki and Hidetoshi Nishimori},
journal={Journal of the Physical Society of Japan},
year={1987},
volume={56},
pages={1568-1576}
}
• Published 15 April 1987
• Physics
• Journal of the Physical Society of Japan
We have performed large-scale numerical simulations for the ± J Ising model on the simple cubic and the square lattices with asymmetric weight of ferromagnetic and antiferromagnetic bonds. The Monte Carlo renormalization group method is used to estimate T c , γ/ν, β/ν and ν at various points along the phase boundary between ferromagnetic and paramagnetic phases including the tricritical point. The obtained values of T c and the resulting phase diagrams of the simple cubic and the square…
42 Citations
The Critical Exponent ν along the Ferromagnetic-Nonferromagnetic Phase Boundary in the Two-Dimensional ± J Ising Model
• Physics
• 1992
The value of the critical exponent ν of the two-dimensional ± J Ising model along the ferromagnetic-nonferromagnetic phase boundary in the p - T plane ( p is the concentration of + J bonds; T is the
Nonequilibrium Relaxation Study of Effect of Randomness on Critical Universality Classes of Ferromagnetic Phase Transitions
• Physics
• 2012
The ferromagnetic critical exponents are estimated along the phase boundary for the gauge glass model in three dimensions. The nonequilibrium relaxation method is applied to estimate the transition
Interfacial approach tod-dimensional ±J Ising models in the neighborhood of the ferromagnetic phase boundary
• Physics
• 1991
Two- and three-dimensional ±J Ising models in the neighborhood of the ferromagnetic phase (FP) boundary in the concentration-temperature (p-T) plane are studied, investigating the size dependence of
Non-Universal Critical Behavior in the Ferromagnetic Transition of the ± J Ising Model
• Physics
• 1999
Ferromagnetic (FM) transition of the ± J Ising model is studied for square and simple-cubic lattices by Monte Carlo simulations. Non-equilibrium relaxation (NER) process of magnetization from the
Phase Diagram of the ±J Ising Model in Two Dimensions
• Physics
• 1987
The ± J Ising model with asymmetric probability weight of ± bonds in two dimensions is studied in the p - T plane by the numerical transfer-matrix method. We calculate finite-width susceptibilities
Phase Diagram of a Short-Range ±J Heisenberg Model in Three Dimensions
• Physics
• 1991
The short-range ± J Heisenberg model with the concentration of ferromagnetic bonds p on a simple cubic lattice is studied using a hybrid Monte-Carlo spin-dynamics (HMCSD) method. Using a finite-size
Magnetic-glassy multicritical behavior of the three-dimensional +- J Ising model
• Physics
• 2007
We consider the three-dimensional $\pm J$ model defined on a simple cubic lattice and study its behavior close to the multicritical Nishimori point where the paramagnetic-ferromagnetic, the
Ferromagnetic Transition of ± J Ising Spin Glass Model on Square Lattice
• Physics
• 1998
The ferromagnetic transition of ± J -Ising spin-glass model on square lattice is studied by using Monte Carlo simulation. At ferromagnetic-bond density p =0.96 where the system shows ferromagnetic
Phase Diagram of Three-Dimensional Site-Random Ising Model
• Physics
• 1997
The three-dimensional site-random Ising model consisting of two types of magnetic ions, A and B, is investigated by means of the exchange Monte Carlo method. The nearest-neighbor interactions are

## References

SHOWING 1-10 OF 19 REFERENCES
Theory of spin glasses
• Physics
• 1975
A new theory of the class of dilute magnetic alloys, called the spin glasses, is proposed which offers a simple explanation of the cusp found experimentally in the susceptibility. The argument is
Geometry-Induced Phase Transition in the ±J Ising Model
We present an argument for the existence of a geometry-induced phase transition in the ± J Ising model on an arbitrary lattice ( d ≥2) with asymmetric probability of ferromagnetic and
Critical behavior of three-dimensional Ising spin-glass model.
• Physics
Physical review letters
• 1985
First results of massive Monte Carlo simulations of the d=3 Ising spin-glass with ±J bond distribution, performed on a fast special purpose computer, are presented. A qualitative change in the
Exact properties of spin glasses. II. Nishimori's line : new results and physical implications
• Physics
• 1985
An exact result for spin glasses, due to Nishimori, is reconsidered. The existence, in the phase diagram, of a subspace where some exact properties can be derived, is generalized to a larger class of
Dynamics of three-dimensional Ising spin glasses in thermal equilibrium.
• Ogielski
• Materials Science, Physics
Physical review. B, Condensed matter
• 1985
The dynamic scaling hypothesis and finite-size scaling explain well the observed temperature and size dependence of the data, and the functional form of the correlation functions is com- patible with the scaling form if corrections to scaling are taken into account.
Critical exponents from field theory
• Physics
• 1980
We present a detailed study of the methods of summation based on Borel transformation and conformai mapping, which we have used to calculate critical exponents of the n -vector model through field
Three-dimensional random-bond Ising model: Phase diagram and critical properties.
• Physics, Medicine
Physical review letters
• 1986
Limites de phases pour les phases ferro, verre de spin and paramagnetique pour ce modele en fonction de the temperature and of the concentration en liaison ferromagnetiques.
Solvable Model of a Spin-Glass
• Physics
• 1975
We consider an Ising model in which the spins are coupled by infinite-ranged random interactions independently distributed with a Gaussian probability density. Both "spinglass" and ferromagnetic
Infinite Number of Order Parameters for Spin-Glasses
This Letter shows that in the mean-field approximation spin-glasses must be described by an infinite number of order parameters in the framework of the replica theory.
Critical behavior of an Ising spin-glass.
• Physics, Medicine
Physical review letters
• 1986
Mise en evidence de transitions a temperature finie en 3D et 4D and d'une transition T=0 en 2D et d'un transition T =0 in 3D, 4D, et 2D.