Transfer-Matrix Monte Carlo Estimates of Critical Points in the Simple Cubic Ising, Planar and Heisenberg Models

The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the statistical noise can be reduced considerably by a similarity transformation of the transfer matrix using a variational estimate of its leading eigenvector, in analogy with a common practice in various quantum Monte Carlo techniques. Here we take the two-dimensional coupled $XY$-Ising model as an example. Furthermore, we calculate interface free energies of finite three-dimensional O($n$) models, for the three cases $n=1$, 2 and 3. Application of finite-size scaling to the numerical results yields estimates of the critical points of these three models. The statistical precision of the estimates is satisfactory for the modest amount of computer time spent

Decoupling in the 1D frustrated quantum XY model and Josephson junction ladders: Ising critical behavior

A generalization of the one-dimensional frustrated quantum XY model is considered in which the inter and intra-chain coupling constants of the two infinite XY (planar rotor) chains have different strengths. The model can describe the superconductor to insulator transition due to charging effects in a ladder of Josephson junctions in a magnetic field with half a flux quantum per plaquette. From a fluctuation-effective action, this transition is expected to be in the universality class of the two-dimensional classical XY-Ising model. The critical behavior is studied using a Monte Carlo transfer matrix applied to the path-integral representation of the model and a finite-size-scaling analysis of data on small system sizes. It is found that, unlike the previous studied case of equal inter and intra-chain coupling constants, the XY and Ising-like excitations of the quantum model decouple for large interchain coupling, giving rise to pure Ising model critical behavior for the chirality order parameter and a superconductor-insulator transition in the universality class of the 2D classical XY model.Comment: 15 pages with figures, RevTex 3.0, INPE-93/00

Magnetization reversal times in the 2D Ising model

We present a theoretical framework which is generally applicable to the study of time scales of activated processes in systems with Brownian type dynamics. This framework is applied to a prototype system: magnetization reversal times in the 2D Ising model. Direct simulation results for the magnetization reversal times, spanning more than five orders of magnitude, are compared with theoretical predictions; the two agree in most cases within 20%.Comment: 9 pages, 8 figure

Conformal Anomaly and Critical Exponents of the XY-Ising Model

We use extensive Monte Carlo transfer matrix calculations on infinite strips of widths $L$ up to 30 lattice spacing and a finite-size scaling analysis to obtain critical exponents and conformal anomaly number $c$ for the two-dimensional $XY$-Ising model. This model is expected to describe the critical behavior of a class of systems with simultaneous $U(1)$ and $Z_2$ symmetries of which the fully frustrated $XY$ model is a special case. The effective values obtained for $c$ show a significant decrease with $L$ at different points along the line where the transition to the ordered phase takes place in a single transition. Extrapolations based on power-law corrections give values consistent with $c=3/2$ although larger values can not be ruled out. Critical exponents are obtained more accurately and are consistent with previous Monte Carlo simulations suggesting new critical behavior and with recent calculations for the frustrated $XY$ model.Comment: 33 pages, 13 latex figures, uses RevTeX 3.

FINITE SIZE SCALING FOR FIRST ORDER TRANSITIONS: POTTS MODEL

The finite-size scaling algorithm based on bulk and surface renormalization of de Oliveira (1992) is tested on q-state Potts models in dimensions D = 2 and 3. Our Monte Carlo data clearly distinguish between first- and second-order phase transitions. Continuous-q analytic calculations performed for small lattices show a clear tendency of the magnetic exponent Y = D - beta/nu to reach a plateau for increasing values of q, which is consistent with the first-order transition value Y = D. Monte Carlo data confirm this trend.Comment: 5 pages, plain tex, 5 EPS figures, in file POTTS.UU (uufiles

Critical behavior of Josephson-junction arrays at f=1/2

The critical behavior of frustrated Josephson-junction arrays at $f=1/2$ flux quantum per plaquette is considered. Results from Monte Carlo simulations and transfer matrix computations support the identification of the critical behavior of the square and triangular classical arrays and the one-dimensional quantum ladder with the universality class of the XY-Ising model. In the quantum ladder, the transition can happen either as a simultaneous ordering of the $Z_2$ and $U(1)$ order parameters or in two separate stages, depending on the ratio between interchain and intrachain Josephson couplings. For the classical arrays, weak random plaquette disorder acts like a random field and positional disorder as random bonds on the $Z_2$ variables. Increasing positional disorder decouples the $Z_2$ and $U(1)$ variables leading to the same critical behavior as for integer $f$.Comment: 9 pages, Latex, workshop on JJA, to appear in Physica

Medium-range interactions and crossover to classical critical behavior

We study the crossover from Ising-like to classical critical behavior as a function of the range R of interactions. The power-law dependence on R of several critical amplitudes is calculated from renormalization theory. The results confirm the predictions of Mon and Binder, which were obtained from phenomenological scaling arguments. In addition, we calculate the range dependence of several corrections to scaling. We have tested the results in Monte Carlo simulations of two-dimensional systems with an extended range of interaction. An efficient Monte Carlo algorithm enabled us to carry out simulations for sufficiently large values of R, so that the theoretical predictions could actually be observed.Comment: 16 pages RevTeX, 8 PostScript figures. Uses epsf.sty. Also available as PostScript and PDF file at http://www.tn.tudelft.nl/tn/erikpubs.htm

Temperature dependence of single particle excitations in a S=1 chain: exact diagonalization calculations compared to neutron scattering experiments

Exact diagonalization calculations of finite antiferromagnetic spin-1 Heisenberg chains at finite temperatures are presented and compared to a recent inelastic neutron scattering experiment for temperatures T up to 7.5 times the intrachain exchange constant J. The calculations show that the excitations at the antiferromagnetic point q=1 and at q=0.5 remain resonant up to at least T=2J, confirming the recent experimental observation of resonant high-temperature domain wall excitations. The predicted first and second moments are in good agreement with experiment, except at temperatures where three-dimensional spin correlations are most important. The ratio of the structure factors at q=1 and at q=0.5 is well predicted for the paramagnetic infinite-temperature limit. For T=2J, however, we found that the experimentally observed intensity is considerably less than predicted. This suggests that domain wall excitations on different chains interact up to temperatures of the order of the spin band width.Comment: 9 pages revtex, submitted to PR

Impurity Energy Level Within The Haldane Gap

An impurity bond $J{'}$ in a periodic 1D antiferromagnetic, spin 1 chain with exchange $J$ is considered. Using the numerical density matrix renormalization group method, we find an impurity energy level in the Haldane gap, corresponding to a bound state near the impurity bond. When $J{'}<J$ the level changes gradually from the edge of the Haldane gap to the ground state energy as the deviation $dev=(J-J{'})/J$ changes from 0 to 1. It seems that there is no threshold. Yet, there is a threshold when $J{'}>J$. The impurity level appears only when the deviation $dev=(J{'}-J)/J{'}$ is greater than $B_{c}$, which is near 0.3 in our calculation.Comment: Latex file,9 pages uuencoded compressed postscript including 4 figure

Correlation decay and conformal anomaly in the two-dimensional random-bond Ising ferromagnet

The two-dimensional random-bond Ising model is numerically studied on long strips by transfer-matrix methods. It is shown that the rate of decay of correlations at criticality, as derived from averages of the two largest Lyapunov exponents plus conformal invariance arguments, differs from that obtained through direct evaluation of correlation functions. The latter is found to be, within error bars, the same as in pure systems. Our results confirm field-theoretical predictions. The conformal anomaly $c$ is calculated from the leading finite-width correction to the averaged free energy on strips. Estimates thus obtained are consistent with $c=1/2$, the same as for the pure Ising model.Comment: RevTeX 3, 11 pages +2 figures, uuencoded, IF/UFF preprin