The random-field Ising model with asymmetric bimodal probability distribution

The Ising model, in the presence of a random field, is investigated within the mean-field approximation based on Landau expansion. The random field is drawn from the bimodal probability distribution P(h)=pδ(h−h₀)+(1−p)δ(h+h₀), where the probability p assumes any value within the interval [0,1], asymmetric distribution. The prevailing transitions are of second-order but, for some values of p and h₀, first-order phase transitions take place for smaller temperatures and higher h₀, thus confirming the existence of a tricritical point. Also, the possible reentrant phenomena in the phase diagram (T−h₀ plane) occur for appropriate values of p and h₀. Using the variational principle, we determine the equilibrium equation for magnetization and solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h₀.     

A first-order phase transition in a three-dimensional vertex model

For a specific three-dimensional vertex model, it is proven that it will show a first-order phase transition. The critical temperature is given in terms of the energy of some local vertex configurations. The approach used is similar to the Nagle approach. Some classes of compounds are considered which may be related to this model.     

Plastic flow in a driven random-field XY model

Plastic depinning and flow in a one-dimensional random-field XY model in the presence of a driving force are investigated numerically. From the analysis of velocity-force and related characteristics, it is found that a scaling relation holds in plastic flow states under strong pinning conditions.     

Low-energy excitations in the three-dimensional random-field Ising model

General conservation equations are derived for 2D dense granular flows from the Euler equation within the Boussinesq approximation. In steady flows, the 2D fields of granular temperature, vorticity and stream function are shown to be encoded in two scalar functions only. We checked such prediction on steady surface flows in a rotating drum simulated through the Non-Smooth Contact Dynamics method even though granular flows are dissipative and therefore not necessarily compatible with Euler equation. Finally, we briefly discuss some possible ways to predict theoretically these two functions using statistical mechanics.     

Quantum fluctuation driven first-order phase transition in weak ferromagnetic metals

In a local Fermi liquid (LFL), we show that there is a line of weak first-order phase transitions between the ferromagnetic and paramagnetic phases due to purely quantum fluctuations. We predict that an instability towards superconductivity is only possible in the ferromagnetic state. At T?=?0 we find a point on the phase diagram where all three phases meet and we call this a quantum triple point (QTP). A simple application of the Gibbs phase rule shows that only these three phases can meet at the QTP. This provides a natural explanation of the absence of superconductivity at this point coming from the paramagnetic side of the phase diagram, as observed in the recently discovered ferromagnetic superconductor, UGe ₂.     

Diagrammatic expansion and metastability in the random-field Ising model

Within the perturbation diagrammatic expansion we discuss the origin of differences in determinations of the lower critical dimension of the random-field Ising model and show that below four dimensions metastability and hysteresis occur. We also explain the occurrence of a quasicritical d=2 behavior at weak random fields, which is responsible for local stability of the ordered state above two dimensions.     

Scaling and self-averaging in the three-dimensional random-field Ising model

We investigate, by means of extensive Monte Carlo simulations, the magnetic critical behavior of the three-dimensional bimodal random-field Ising model at the strong disorder regime. We present results in favor of the two-exponent scaling scenario, [`(h)]\bar{\eta} = 2η, where η and [`(h)]\bar{\eta} are the critical exponents describing the power-law decay of the connected and disconnected correlation functions and we illustrate, using various finite-size measures and properly defined noise to signal ratios, the strong violation of self-averaging of the model in the ordered phase.     

Hysteresis in the random-field Ising model and bootstrap percolation

We study hysteresis in the random-field Ising model with an asymmetric distribution of quenched fields, in the limit of low disorder in two and three dimensions. We relate the spin flip process to bootstrap percolation, and show that the characteristic length for self-averaging L small star, filled increases as exp[exp(J/Delta)] in 2D, and as exp(exp[exp(J/Delta)]) in 3D, for disorder strength Delta much less than the exchange coupling J. For system size 1infinity for both square and cubic lattices. For lattices with coordination number 3, the limiting magnetization shows no jump, and h(coer) tends to J.     

Nonequilibrium first-order phase transition in semiconductor system driven by colored noise

We examine the mechanisms of action of colored multiplicative noise in a positionally disordered semiconductor with Moss–Burstein shift. It is shown that the action of multiplicative noise causes nonequilibrium first-order phase transition of the disorder–order-type in electron subsystem of semiconductor. There are relatively little changes in a condensed matter at such phase transitions, but the electron subsystem undergoes a strong reorganization. The steady photocarriers concentration distribution is studied within a unified colored-noise approximation.     

Ising transition driven by frustration in a 2D classical model with continuous symmetry

We study the thermal properties of the classical antiferromagnetic Heisenberg model with both nearest (J1) and next-nearest (J2) exchange couplings on the square lattice by extensive Monte Carlo simulations. We show that, for J2/J1>1/2, thermal fluctuations give rise to an effective Z2 symmetry leading to a finite-temperature phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that T(c)-->0 with an infinite slope when J2/J1-->1/2.     

Depinning of a domain wall in the 2d random-field Ising model

We report studies of the behaviour of a single driven domain wall in the 2-dimensional non-equilibrium zero temperature random-field Ising model, closely above the depinning threshold. It is found that even for very weak disorder, the domain wall moves through the system in percolative fashion. At depinning, the fraction of spins that are flipped by the proceeding avalanche vanishes with the same exponent as the infinite percolation cluster in percolation theory. With decreasing disorder strength, however, the size of the critical region decreases. Our numerical simulation data appear to reflect a crossover behaviour to an exponent at zero disorder strength. The conclusions of this paper strongly rely on analytical arguments. A scaling theory in terms of the disorder strength and the magnetic field is presented that gives the values of all critical exponent except for one, the value of which is estimated from scaling arguments. Received: 13 February 1998 / Accepted: 30 March 1998     

On the phase transition of the Ising gauge model

We study the Ising gauge model in dimensionsD2. In addition to the plaquette coupling of this model we introduce a nearest neighbour ferromagnetic Ising coupling. By that means the local gauge symmetry is removed while the global symmetry of the Ising model is still present. The phase diagram of the model is found by using general arguments as well as Monte-Carlo methods. The gauge phase of the model is characterized by the presence of a topological excitation (defect) which has no influence on any local physical quantity.     

Modulated structure-paramagnet phase transition in the anisotropic Ising model with competing interactions

Long-period modulated structures are investigated by means of Monte Carlo methods within the anisotropic Ising model with competing interactions (the ANNNI model). The amplitude of the modulated phase is proposed as a new order parameter for describing modulated structures. It is shown that the amplitude used as an order parameter allows properties of the modulated phase-paramagnet phase transition to be investigated.