Depinning Transition of a Two Dimensional Vortex Lattice in a Commensurate Periodic Potential

We use Monte Carlo simulations of the 2D one component Coulomb gas on a triangular lattice, to study the depinning transition of a 2D vortex lattice in a commensurate periodic potential. A detailed finite size scaling analysis indicates this transition to be first order. No significant changes in behavior were found as vortex density was varied over a wide range.Comment: 5 pages, 8 figures. Revised discussion of correlation length exponent using a more accurate finite size scaling analysis. New figs. 5 and 6. Old figs. 6 and 7 now figs. 7 and

Finite-Size Scaling Study of the Surface and Bulk Critical Behavior in the Random-Bond 8-state Potts Model

The self-dual random-bond eight-state Potts model is studied numerically through large-scale Monte Carlo simulations using the Swendsen-Wang cluster flipping algorithm. We compute bulk and surface order parameters and susceptibilities and deduce the corresponding critical exponents at the random fixed point using standard finite-size scaling techniques. The scaling laws are suitably satisfied. We find that a belonging of the model to the 2D Ising model universality class can be conclusively ruled out, and the dimensions of the relevant bulk and surface scaling fields are found to take the values $y_h=1.849$, $y_t=0.977$, $y_{h_s}=0.54$, to be compared to their Ising values: 15/8, 1, and 1/2.Comment: LaTeX file with Revtex, 4 pages, 4 eps figures, to appear in Phys. Rev. Let

SURFACE INDUCED FINITE-SIZE EFFECTS FOR FIRST ORDER PHASE TRANSITIONS

We consider classical lattice models describing first-order phase transitions, and study the finite-size scaling of the magnetization and susceptibility. In order to model the effects of an actual surface in systems like small magnetic clusters, we consider models with free boundary conditions. For a field driven transition with two coexisting phases at the infinite volume transition point $h=h_t$, we prove that the low temperature finite volume magnetization m_{\free}(L,h) per site in a cubic volume of size $L^d$ behaves like m_\free(L,h)=\frac{m_++m_-}2 + \frac{m_+-m_-}2 \tanh \bigl(\frac{m_+-m_-}2\,L^d\, (h-h_\chi(L))\bigr)+O(1/L), where $h_\chi(L)$ is the position of the maximum of the (finite volume) susceptibility and $m_\pm$ are the infinite volume magnetizations at $h=h_t+0$ and $h=h_t-0$, respectively. We show that $h_\chi(L)$ is shifted by an amount proportional to $1/L$ with respect to the infinite volume transitions point $h_t$ provided the surface free energies of the two phases at the transition point are different. This should be compared with the shift for periodic boun\- dary conditons, which for an asymmetric transition with two coexisting phases is proportional only to $1/L^{2d}$. One also consider the position $h_U(L)$ of the maximum of the so called Binder cummulant U_\free(L,h). While it is again shifted by an amount proportional to $1/L$ with respect to the infinite volume transition point $h_t$, its shift with respect to $h_\chi(L)$ is of the much smaller order $1/L^{2d}$. We give explicit formulas for the proportionality factors, and show that, in the leading $1/L^{2d}$ term, the relative shift is the same as that for periodic boundary conditions.Comment: 65 pages, amstex, 1 PostScript figur

Interplay of quantum and thermal fluctuations in a frustrated magnet

We demonstrate the presence of an extended critical phase in the transverse field Ising magnet on the triangular lattice, in a regime where both thermal and quantum fluctuations are important. We map out a complete phase diagram by means of quantum Monte Carlo simulations, and find that the critical phase is the result of thermal fluctuations destabilising an order established by the quantum fluctuations. It is separated by two Kosterlitz-Thouless transitions from the paramagnet on one hand and the quantum-fluctuation driven three-sublattice ordered phase on the other. Our work provides further evidence that the zero temperature quantum phase transition is in the 3d XY universality class.Comment: 9 pages, revtex

Critical behavior of the frustrated antiferromagnetic six-state clock model on a triangular lattice

We study the anti-ferromagnetic six-state clock model with nearest neighbor interactions on a triangular lattice with extensive Monte-Carlo simulations. We find clear indications of two phase transitions at two different temperatures: Below $T_I$ a chirality order sets in and by a thorough finite size scaling analysis of the specific heat and the chirality correlation length we show that this transition is in the Ising universality class (with a non-vanishing chirality order parameter below $T_I$). At $T_{KT}(<T_I)$ the spin-spin correlation length as well as the spin susceptibility diverges according to a Kosterlitz-Thouless (KT) form and spin correlations decay algebraically below $T_{KT}$. We compare our results to recent x-ray diffraction experiments on the orientational ordering of CF$_3$Br monolayers physisorbed on graphite. We argue that the six-state clock model describes the universal feature of the phase transition in the experimental system and that the orientational ordering belongs to the KT universality class.Comment: 8 pages, 9 figure

First-Order Phase Transition with Breaking of Lattice Rotation Symmetry in Continuous-Spin Model on Triangular Lattice

Using a Monte Carlo method, we study the finite-temperature phase transition in the two-dimensional classical Heisenberg model on a triangular lattice with or without easy-plane anisotropy. The model takes account of competing interactions: a ferromagnetic nearest-neighbor interaction $J_1$ and an antiferromagnetic third nearest-neighbor interaction $J_3$. As a result, the ground state is a spiral spin configuration for $-4 < J_1/J_3 < 0$. In this structure, global spin rotation cannot compensate for the effect of 120-degree lattice rotation, in contrast to the conventional 120-degree structure of the nearest-neighbor interaction model. We find that this model exhibits a first-order phase transition with breaking of the lattice rotation symmetry at a finite temperature. The transition is characterized as a $Z_2$ vortex dissociation in the isotropic case, whereas it can be viewed as a $Z$ vortex dissociation in the anisotropic case. Remarkably, the latter is continuously connected to the former as the magnitude of anisotropy decreases, in contrast to the recent work by Misawa and Motome [J. Phys. Soc. Jpn. \textbf{79} (2010) 073001.] in which both the transitions were found to be continuous.Comment: 11pages, 16figures, accepted to JPS

Critical Behavior of the 3d Random Field Ising Model: Two-Exponent Scaling or First Order Phase Transition?

In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the random fields it is found that the correlation length $\xi$ diverges with an exponent $\nu=1.1\pm0.2$ at the critical temperature and that $\chi\sim\xi^{2-\eta}$ with $\eta=0.50\pm0.05$ for the connected susceptibility and $\chi_{\rm dis}\sim\xi^{4-\bar{\eta}}$ with $\bar{\eta}=1.03\pm0.05$ for the disconnected susceptibility. Together with the amplitude ratio $A=\lim_{T\to T_c}\chi_{\rm dis}/\chi^2(h_r/T)^2$ being close to one this gives further support for a two exponent scaling scenario implying $\bar{\eta}=2\eta$. The magnetization behaves discontinuously at the transition, i.e. $\beta=0$, indicating a first order transition. However, no divergence for the specific heat and in particular no latent heat is found. Also the probability distribution of the magnetization does not show a multi-peak structure that is characteristic for the phase-coexistence at first order phase transition points.Comment: 14 pages, RevTeX, 11 postscript figures (fig9.ps and fig11.ps should be printed separately

Aperiodicity-Induced Second-Order Phase Transition in the 8-State Potts Model

We investigate the critical behavior of the two-dimensional 8-state Potts model with an aperiodic distribution of the exchange interactions between nearest-neighbor rows. The model is studied numerically through intensive Monte Carlo simulations using the Swendsen-Wang cluster algorithm. The transition point is located through duality relations, and the critical behavior is investigated using FSS techniques at criticality. For strong enough fluctuations of the aperiodic sequence under consideration, a second order phase transition is found. The exponents $\beta/\nu$ and $\gamma /\nu$ are obtained at the new fixed point.Comment: LaTeX file with Revtex, 4 pages, 5 eps figures, to appear in Phys. Rev. Let

Universal Short-Time Dynamics in the Kosterlitz-Thouless Phase

We study the short-time dynamics of systems that develop ``quasi long-range order'' after a quench to the Kosterlitz-Thouless phase. With the working hypothesis that the ``universal short-time behavior'', previously found in Ising-like systems, also occurs in the Kosterlitz-Thouless phase, we explore the scaling behavior of thermodynamic variables during the relaxational process following the quench. As a concrete example, we investigate the two-dimensional $6$-state clock model by Monte Carlo simulation. The exponents governing the magnetization, the second moment, and the autocorrelation function are calculated. From them, by means of scaling relations, estimates for the equilibrium exponents $z$ and $\eta$ are derived. In particular, our estimates for the temperature-dependent anomalous dimension $\eta$ that governs the static correlation function are consistent with existing analytical and numerical results and, thus, confirm our working hypothesis.Comment: 16 pages, 9 postscript figures, REVTEX 3.0, submitted to Phys. Rev.

Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries

We present a numerical study of 2D random-bond Potts ferromagnets. The model is studied both below and above the critical value $Q_c=4$ which discriminates between second and first-order transitions in the pure system. Two geometries are considered, namely cylinders and square-shaped systems, and the critical behavior is investigated through conformal invariance techniques which were recently shown to be valid, even in the randomness-induced second-order phase transition regime Q>4. In the cylinder geometry, connectivity transfer matrix calculations provide a simple test to find the range of disorder amplitudes which is characteristic of the disordered fixed point. The scaling dimensions then follow from the exponential decay of correlations along the strip. Monte Carlo simulations of spin systems on the other hand are generally performed on systems of rectangular shape on the square lattice, but the data are then perturbed by strong surface effects. The conformal mapping of a semi-infinite system inside a square enables us to take into account boundary effects explicitly and leads to an accurate determination of the scaling dimensions. The techniques are applied to different values of Q in the range 3-64.Comment: LaTeX2e file with Revtex, revised versio