Monte Carlo Study of Mixed-Spin S=(1/2,1) Ising Ferrimagnets

We investigate Ising ferrimagnets on square and simple-cubic lattices with exchange couplings between spins of values S=1/2 and S=1 on neighbouring sites and an additional single-site anisotropy term on the S=1 sites. Based mainly on a careful and comprehensive Monte Carlo study, we conclude that there is no tricritical point in the two--dimensional case, in contradiction to mean-field predictions and recent series results. However, evidence for a tricritical point is found in the three-dimensional case. In addition, a line of compensation points is found for the simple-cubic, but not for the square lattice.Comment: 14 pages, 11 figure

Interfacial adsorption phenomena of the three-dimensional three-state Potts model

We study the interfacial adsorption phenomena of the three-state ferromagnetic Potts model on the simple cubic lattice by the Monte Carlo method. Finite-size scaling analyses of the net-adsorption yield the evidence of the phase transition being of first-order and $k_{\rm B} T_{\rm C} / J = 1.8166 (2)$.Comment: 14 page

Determination of the Critical Exponents for the Isotropic-Nematic Phase Transition in a System of Long Rods on Two-dimensional Lattices: Universality of the Transition

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior and universality for the isotropic-nematic phase transition in a system of long straight rigid rods of length $k$ ($k$-mers) on two-dimensional lattices. The nematic phase, characterized by a big domain of parallel $k$-mers, is separated from the isotropic state by a continuous transition occurring at a finite density. The determination of the critical exponents, along with the behavior of Binder cumulants, indicate that the transition belongs to the 2D Ising universality class for square lattices and the three-state Potts universality class for triangular lattices.Comment: 7 pages, 8 figures, uses epl2.cls, to appear in Europhysics Letter

Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet

We investigate the effects of quenched bond randomness on the critical properties of the two-dimensional ferromagnetic Ising model embedded in a triangular lattice. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method. In the first part of our study we present the finite-size scaling behavior of the pure model, for which we calculate the critical amplitude of the specific heat's logarithmic expansion. For the disordered system, the numerical data and the relevant detailed finite-size scaling analysis along the lines of the two well-known scenarios - logarithmic corrections versus weak universality - strongly support the field-theoretically predicted scenario of logarithmic corrections. A particular interest is paid to the sample-to-sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality.Comment: 10 pages, 8 figures, slightly revised version as accepted for publication in Phys. Rev.

Anisotropic Lifshitz Point at O(ϵL2)O(\epsilon_L^2)

We present the critical exponents $\nu_{L2}$, $\eta_{L2}$ and $\gamma_{L}$ for an $m$-axial Lifshitz point at second order in an $\epsilon_{L}$ expansion. We introduced a constraint involving the loop momenta along the $m$-dimensional subspace in order to perform two- and three-loop integrals. The results are valid in the range $0 \leq m < d$. The case $m=0$ corresponds to the usual Ising-like critical behavior.Comment: 10 pages, Revte

Interfacial adsorption in Potts models on the square lattice

We study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) $q$-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial adsorption, the critical behavior, including corrections to scaling, are analyzed. The role of randomness is scrutinized. Results are discussed applying scaling arguments and invoking findings for bulk critical properties. In all studied cases, i.e., $q = 3$, $4$, and $q = 8$, the spread of the interfacial adsorption profiles is observed to increase linearly with the lattice size at the bulk transition point.Comment: 6 pages, 6 eps figures, 1 table, minor corrections, accepted for publication in Eur. Phys. J.

Commensurate and modulated magnetic phases in orthorhombic A1C60

Competing magnetically ordered structures in polymerized orthorhombic A1C60 are studied. A mean-field theory for the equilibrium phases is developed using an Ising model and a classical Heisenberg model to describe the competition between inter- and intra-chain magnetic order in the solid. In the Ising model, the limiting commensurate one-dimensional and three-dimensional phases are separated by a commensurate three-sublattice state and by two sectors containing higher-order commensurate phases. For the Heisenberg model the quasi-1D phase is never the equilibrium state; instead the 3D commensurate phases exhibits a transition to a continuum of coplanar spiral magnetic phases.Comment: 11 pages REVTeX 3.0 plus 4 figures appende

Lifting of Multiphase Degeneracy by Quantum Fluctuations

We study the effect of quantum fluctuations on the multiphase point of the Heisenberg model with first- and second-neighbor competing interactions and strong uniaxial spin anisotropy $D$. By studying the structure of perturbation theory we show that the multiphase degeneracy which exists for $S=\infty$ (i.e., for the ANNNI model) is lifted and that the effect of quantum fluctuations is to stabilize a sequence of phases of wavelength 4,6,8,...~. This sequence is probably an infinite one. We also show that quantum fluctuations can mediate an infinite sequence of layering transitions through which an interface can unbind from a wall.Comment: 55 pages ReVTeX (encoded with uufiles) + 17 uuencoded figure

Step-wise responses in mesoscopic glassy systems: a mean field approach

We study statistical properties of peculiar responses in glassy systems at mesoscopic scales based on a class of mean-field spin-glass models which exhibit 1 step replica symmetry breaking. Under variation of a generic external field, a finite-sized sample of such a system exhibits a series of step wise responses which can be regarded as a finger print of the sample. We study in detail the statistical properties of the step structures based on a low temperature expansion approach and a replica approach. The spacings between the steps vanish in the thermodynamic limit so that arbitrary small but finite variation of the field induce infinitely many level crossings in the thermodynamic limit leading to a static chaos effect which yields a self-averaging, smooth macroscopic response. We also note that there is a strong analogy between the problem of step-wise responses in glassy systems at mesoscopic scales and intermittency in turbulent flows due to shocks.Comment: 50 pages, 18 figures, revised versio

Infinitesimal incommensurate stripe phase in an axial next-nearest-neighbor Ising model in two dimensions

An axial next-nearest-neighbor Ising (ANNNI) model is studied by using the non-equilibrium relaxation method. We find that the incommensurate stripe phase between the ordered phase and the paramagnetic phase is negligibly narrow or may vanish in the thermodynamic limit. The phase transition is the second-order transition if approached from the ordered phase, and it is of the Kosterlitz-Thouless type if approached from the paramagnetic phase. Both transition temperatures coincide with each other within the numerical errors. The incommensurate phase which has been observed previously is a paramagnetic phase with a very long correlation length (typically $\xi\ge 500$). We could resolve this phase by treating very large systems ($\sim 6400\times 6400$), which is first made possible by employing the present method.Comment: 12 pages, 10 figures. To appear in Phys.Rev.