Monte Carlo Calculation of Free Energy, Critical Point, and Surface Critical Behavior of Three-Dimensional Heisenberg Ferromagnets

A transfer-matrix Monte Carlo technique is developed to compute the free energy of three-dimensional, classical Heisenberg ferromagnets. From the free energy of systems with periodic and antiperiodic boundary conditions, helicity moduli are calculated. From these the critical couplings for simple-cubic (sc) and face-centered-cubic lattices are estimated by use of finite-size scaling. For the simple-cubic lattice, the critical dimension of the surface magnetization is estimated with standard Monte Carlo methods, yielding a result in excellent agreement with the ε-expansion work of Diehl and Nüsser

Gap of the Linear Spin-1 Heisenberg Antiferromagnet: A Monte Carlo Calculation

We have performed Monte Carlo calculations of the energies of several low-lying energy states of one-dimensional, spin-1 Heisenberg antiferromagnets with linear sizes up to n=32. Our results support Haldane’s prediction that a gap exists in the excitation spectrum for n→∞. .A

Conformal Invariance, the Central Charge, and Universal Finite-Size Amplitudes at Criticality

We show that for conformally invariant two-dimensional systems, the amplitude of the finite-size corrections to the free energy of an infinitely long strip of width L at criticality is linearly related to the conformal anomaly number c, for various boundary conditions. The result is confirmed by renormalization-group arguments and numerical calculations. It is also related to the magnitude of the Casimir effect in an interacting one-dimensional field theory, and to the low-temperature specific heat in quantum chains

Unusual Critical Behavior in a Bilinear‐Biquadratic Exchange Hamiltonian

We have performed a variety of numerical studies on the general bilinear‐biquadratic spin‐1 Hamiltonian H/J=∑ N i=1[S i ⋅S i+1 −β(S i ⋅S i+1)2], over the range 0≤β≤∞. The model is Bethe Ansatz integrable at the special point β=1, where the spectrum is gapless, but is otherwise believed to be nonintegrable. Affleck has predicted that an excitation gap opens up linearly in the vicinity of β=1. Our studies involving spectral excitations (dispersion spectra), scaled‐gap, and finite‐size scaling calculations are not consistent with the Affleck prediction. The situation appears complex, with novel crossover effects occurring in both regimes, ββ\u3e1, complicating the analysis

Critical Behaviour of Some 2D Lattice Models

The density series of the non-interacting hard-square lattice gas model are reanalyzed by the ratio, Dlog Padé and differential approximant methods. The problem of poor consistency between series and other results is resolved. Transfer matrix calculations are performed, implementing both finite-size scaling and conformal invariance. Very accurate estimates of the critical exponents y$\text{}_{t}$, and y$\text{}_{h}$ are obtained in agreement with Ising universality. Furthermore, an improvement of the value of the critical density ρ$\text{}_{c}$ is found. In addition, the universal critical-point ratios of the square of the second and the fourth moment of the magnetization for ferromagnetic Ising models on the square and on the triangular lattice with periodic boundary conditions are reported

Heisenberg Antiferromagnetic Chains: Quantum-Classical Crossover

An unusual crossover mechanism has been discovered by numerical investigation of the dispersion spectrum of Heisenberg antiferromagnetic chains with various spin values in a magnetic field. This result is reflected in novel behavior of static properties such as the integrated intensity. A study of various excitation gaps using finite chain calculations extended by quantum Monte Carlo studies indicates unusual behaviour in the T=0 magnetization isotherms