Quenched bond-dilute Ising ferromagnet in square lattice: Thermodynamical properties

Within an effective field framework which substantially improves the Molecular Field Approximation, we calculate the phase diagram, magnetization, specific heat and susceptibility associated with the quenched bond-dilute Ising ferromagnet in square lattice. The results are qualitatively (and within certain extent quantitatively) satisfactory; in particular the effects, on the specific heat and susceptibility, of the (eventually) coexisting finite and infinite clusters are exhibited.     

Critical surface of the quenched bond-diluted cubic model in self-dual lattice: Renormalization group approach

Summary We propose a quite simple real-space renormalization group, which enables us to calculate (for the first time, as far as we know, and presumably with high precision) the critical surface of the quenched bond-diluted discreteN-vector ferromagnet in a self-dual lattice.     

Self-dual planar lattice Ising ferromagnet within generalized thermostatistics

Within a generalized thermostatistics which allows for nonextensivity, we calculate the phase diagram and the correlation length critical exponent ν for the Ising ferromagnet in a self-dual hierarchical lattice which mimics the square lattice.     

Phase diagrams of a quenched site-diluted and bond-mixed Ising ferromagnet with a transverse field

Within the framework of an effective-field theory, the phase diagram is investigated in a quenched site-diluted and bond-mixed Ising ferromagnet with a transverse field on the square lattice; the effect of frustration is discussed.     

Critical behavior in the amorphous Ising ferromagnet with a random field

Within the differential operator method and the effective-field approximation, the critical behaviour of the amorphous Ising ferromagnet with a random field is studied. Tricritical points and reentrant phenomena are discussed. The influence of the random field and the amorphization on the transition temperature is also investigated.     

Critical properties of the three-dimensional frustrated Ising model on a cubic lattice

The critical properties of the three-dimensional fully frustrated Ising model on a cubic lattice are investigated by the Monte Carlo method. The critical exponents α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length), as well as the Fisher exponent η, are calculated in the framework of the finite-size scaling theory. It is demonstrated that the three-dimensional frustrated Ising model on a cubic lattice forms a new universality class of the critical behavior.     

Critical behavior in the dense planar Nambu--Jona-Lasinio model

We present results of a Monte Carlo simulation of a (2+1)-dimensional Nambu-Jona-Lasinio model. In the vacuum phase, the diquark condensate vanishes linearly as a function of diquark source j as expected, but simulations in a region with nonzero baryon density suggest a power-law scaling infinity j(alpha) and hence a critical system for all mu > mu(c). There is no signal for superfluidity. Comparisons are drawn with the pseudogap phase in cuprate superconductors. We also measure the dispersion relation E(k) for fermionic excitations, and find results consistent with a sharp Fermi surface. Any gap Delta is constrained to be much less than the constituent quark mass scale Sigma(0).     

Critical behavior in anisotropic cubic systems with long-range interactions

Effects of the potential range of interaction to critical behaviors of anisotropic cubic systems are investigated by means of the Callan-Symanzik equations. As the static critical behavior the stability of fixed points, the critical exponents η^C, γ^C, φ^C_s and φ^C_c, and the equation of state are also investigated. As the dynamic critical behavior the dynamic critical exponent z_φ is derived based on the time-dependent Ginzburg-Landau stochastic model. The two- and three-dimensional critical behaviors are discussed.     

Quantum spin model of a cubic ferromagnet in a magnetic field

The zero temperature phase diagram of a one-dimensional ferromagnet with cubic single ion anisotropy in an external magnetic field is studied. The mean-field approximation and the density-matrix renormalization group method are applied. Two phases at finite magnetic fields are identified: a canted phase with spontaneously broken symmetry and a phase with magnetization along the magnetic field. Both methods predict that the canted phase exists even for the single-ion anisotropy strong enough to destroy the magnetic order at zero magnetic field. In contrast to the mean-field theory, the density-matrix renormalization group predicts a reentrant behavior for the model. The character of the phase transition at finite magnetic field has also been considered and the critical index has been found. Received 9 May 2000 and Received in final form 5 July 2000     

Microscopic theory of hydrodynamic modes in a planar ferromagnet

The hydrodynamic equations for an easy-plane (planar) ferromagnet are derived by analogy with the hydrodynamics of liquid helium. The relaxation of the magnitude of an order parameter is taken into account.The derivation is based on microscopic dynamics and the nonequilibrium statistical operator method. The hydrodynamic equations are generally nonlocal in space and in time and hold for all T<T_c.Transport coefficients are expressed in terms of time correlation functions and their symmetry properties are investigated.     

Critical behavior of a three-state Potts model on a Voronoi lattice

We use the single-histogram technique to study the critical behavior of the three-state Potts model on a (random) Voronoi-Delaunay lattice with size ranging from 250 to 8 000 sites. We consider the effect of an exponential decay of the interactions with the distance, , with a>0, and observe that this system seems to have critical exponents and which are different from the respective exponents of the three-state Potts model on a regular square lattice. However, the ratio remains essentially the same. We find numerical evidences (although not conclusive, due to the small range of system size) that the specific heat on this random system behaves as a power-law for a=0 and as a logarithmic divergence for a=0.5 and a=1.0 Received 5 April 2000     

Critical behavior of a degenerate ferromagnet in a uniaxial random field: Exact results in a space of arbitrary dimension

The critical behavior of the transverse (with respect to the field) magnetization component in classical degenerate magnets with only nearest-neighbors interaction in a uniaxial random magnetic field at zero temperature is found exactly. For a Gaussian distribution of the random field the asymptotic transverse magnetization in strong fields does not depend on the dimension of the space and is of the form m _⊥ ∝ 1nh ₀/h ₀ ² , where h ₀ is the width of the distribution. For a bimodal distribution, where only the field direction is random and the amplitude is fixed, the transverse magnetization behaves as m _⊥∝exp(−const/(H _c −H) ^D/2), where H is the amplitude of the random field, D is the dimension of the space, and H _c is the critical field. Zh. éksp. Teor. Fiz. 115, 2143–2159 (June 1999)     

Critical properties of the antiferromagnetic layered Ising model on a cubic lattice with competing interactions

The critical properties of the antiferromagnetic layered Ising model on a cubic lattice with regard to the nearest-neighbor and next-nearest-neighbor interactions are investigated by the Monte Carlo method using the replica algorithm. The investigations are carried out for the ratios of exchange nearest-neighbor and next-nearest-neighbor interactions r = J ₂/J ₁ in the range of 0 ≤ r ≤ 1.0. Using the finite-size scaling theory, the static critical indices of specific heat α, order parameter β, susceptibility γ, correlation radius ν, and Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is retained in the range of 0 ≤ r ≤ 0.4. It is established that the change in the next-nearest-neighbor interaction value in this model in the range of r > 0.8 leads to the same universality class as the three-dimensional fully frustrated Ising model on the cubic lattice.

     

Critical behavior of two-dimensional magnetic lattice gas model

Using Monte Carlo simulations and finite-size scaling, we investigate the critical behavior of two-dimensional magnetic lattice gas at densities ρ = 0.90, 0.95, 1.0. There is a ferromagnetic phase transition at each density. As expected, the critical temperature T _c depends on system density ρ. Unexpectedly, there is a density dependence of the critical exponent of correlation length ν. For densities ρ = 0.90,0.95,1.0, we obtain the inverse of critical exponent 1/ν = 0.835(5), 0.905(5), 1.00(1) respectively. It is found that the ratios of critical exponent β/ν and γ/ν of magnetization and susceptibility are independent of density.     

Drift mobility correlation in a simple cubic lattice

A Monte Carlo method is described for the calculation of the drift mobility of interacting ions on a simple cubic lattice in an electric field. This formalism provides a useful operational model for electromigration in interstitial solid solutions. The results, which show a correlation in the drift of the ions, can be interpreted either in terms of a deviation from the Nernst-Einstein relation in the sense of vacancy wind effects or as an intrinsic correlation effect in the diffusion coefficient of the charge carriers. It is also shown that the usual tracer correlation factor can be calculated upon subtracting the square of the average drifts from the average squared displacements.     

Critical behavior of a mixed ferrimagnetic ternary alloy on the Bethe lattice

The critical behavior of the mixed Ising model of the type AB _p C_1−p ternary alloy consisting of spins σ = 1/2, S = 1, and m = 3/2 is investigated on the Bethe lattice by using the exact recursion relations. The exact expressions for the magnetizations and magnetic susceptibilities are found, and the thermal behaviors of the magnetizations and susceptibilities are studied. The magnetizations and susceptibilities have also been investigated as functions of the crystal-field interaction or single-ion anisotropy. The phase diagram has been constructed according to which the system always undergoes a second-order phase transition for the coordination number q ≤ 3 and second-and first-order phase transitions for q > 3; hence, the system has a tricritical point. The system also exhibits reentrant behaviors. The text was submitted by the authors in English.     

Potts ferromagnet: Transformations and critical exponents in planar hierarchical lattices

We prove that the duality transformation for a Potts ferromagnet on two-rooted planar hierarchical lattices (HL) preserves the thermal eigenvalue. This leads to a relation between the correlation length critical exponents of a HL and its corresponding dual lattice. Using hyperscaling, we show that their specific heat critical exponents coincide. For a smaller class of HL—namely of diamond and tress types—we prove that another transformation also preserves and .     

Critical behavior of the 3D Ising model on a poissonian random lattice

The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D ferromagnetic Ising model on 3D Voronoi-Delauney lattices. It is assumed that the coupling factor J varies with the distance r between the first neighbors as J(r)∝e^−ar, with a≥0. The critical exponents γ/ν, β/ν, and ν are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure 3D ferromagnetic Ising model.     

Critical behavior of anisotropic cubic systems with long- and short-range interactions

Critical phenomena in anisotropic cubic N-component spin systems with long- and short-range interactions are investigated and discussed in the regions of weakly long-range, intermediate-range, range, and the long-range potentials. The expressions for the eigenvalues and the critical exponents (n,γ and crossover exponents) in these three regions are derived and their stability is discussed. These results of the systems are compared with those of the same isotropic systems.