Baxter-Wu Model Research Articles

A Monte Carlo renormalisation group calculation of the dynamical exponent z for the Baxter-Wu model

A Monte Carlo renormalisation group technique is used to calculate time correlation functions for the Baxter-Wu model. Initial lattices of size 24*24 and 48*48 are used. The value obtained for the dynamical exponent z is in good agreement with that obtained by means of standard Monte Carlo methods.

Three-spin models in two dimensions: generalisations of the Baxter-Wu model

The authors show that a large class of two-dimensional pure three-spin statistical mechanical models can be analysed using a vector Coulomb gas. This can be done with the same methods previously applied to the 2D XY model and results of similar rigour obtained. The models considered here are generalisations of the Baxter-Wu (1973) model, with the Hamiltonian being given by a sum of three-spin interactions over a triangular lattice.

Triplet Z( N) model in a triangular lattice

The phase structure of a class of two-dimensional spin models with three-body interactions defined on a triangular lattice is studied. This class of models, containing the Baxter-Wu model as a special case, is shown to share the duality properties of a wide class of spin theories in two and three dimensions and the Z( N) gauge theory in four dimensions. Like these models, our theory is shown to possess a massless, Kosterlitz-Thouless-like phase when the number of available spin states exceeds a critical value.

Monte Carlo renormalization-group study of the Baxter-Wu model

The effectiveness of a Monte Carlo renormalization-group method is studied by applying it to the Baxter-Wu model (Ising spins on a triangular lattice with three-spin interactions). The calculations yield three relevant eigenvalues in good agreement with exact or conjectured results. We demonstrate that the method is capable of distinguishing between models expected to be in the same universality class, when one of them (four-state Potts) exhibits logarithmic corrections to the usual power-law singularities and the other (Baxter-Wu) does not.

Z(N) generalisation of the Baxter-Wu model

A two-dimensional model of the dynamics of Z(N) spins on a triangular lattice with three-body interactions is analysed. The properties of the model under duality are shown to be identical to those of a wide class of models in two, three and four dimensions. Monte Carlo simulations reveal the existence of three phases for N>4, with an intermediate phase which is most likely soft.

Random Baxter-Wu model: Duality relations and the replica method

Replica partition function for quenched bond disorder in a Baxter-Wu system is investigated. Its duality relations are obtained which yield exact values for the percolation concentration p c. Arguments used by Domany and others for the bond-random Ising model are extended and refined and T c( p) near p c is calculated. Exact results for the equiconcentration case with arbitrary (positive) bonds J A and J B are also obtained. Finally, the possibility of a Baxter-Wu spin-glass is mooted and a qualitative estimate for its location is given.

Finite size scaling analysis of the dilute Baxter-Wu model

The finite size scaling method is used to study the critical properties of the spin-1 Baxter-Wu model as function of the fugacity, z, of the vacant (spin zero) sites. For z=0, the thermal exponent converges very quickly to the (exact) value yt=3/2. For z>0, yt monotonically increases beyond the value 2. This increase is interpreted as indicating a first-order transition. Out of several possible renormalisation group flows, the results seem to favour the one in which the critical Baxter-Wu Hamiltonian flows to the fixed point of the 4-state Potts model, with the amplitude of the marginal operator equal to zero.

Critical behavior of the Baxter-Wu model with quenched impurities

We have used an importance-sampling Monte Carlo technique to study the Baxter-Wu model with various fractions of the lattice sites occupied by random, quenched, nonmagnetic, site impurities. We found the system had long-time fluctuations which were caused by the creation and motion of domain boundaries. For this reason our study required the use of a large number of Monte Carlo steps per spin. The data were analyzed using finite-size scaling to extract the infinite-lattice critical exponents and critical amplitudes from the Monte Carlo simulation of finite lattices. This analysis of the data for the pure Baxter-Wu model yielded results which agreed well with exact results and series-expansion predictions. The addition of quenched site impurities caused a dramatic change in the critical behavior. The pure-lattice critical exponents ($\ensuremath{\nu}=\frac{2}{3}$, $\ensuremath{\alpha}=\frac{2}{3}$, ${\ensuremath{\gamma}}_{m}\ensuremath{\simeq}1.17$) change upon the addition of only a few percent impurities to $\ensuremath{\nu}=1.00\ifmmode\pm\else\textpm\fi{}0.07$, $\ensuremath{\alpha}\ensuremath{\lesssim}0.0$, and ${\ensuremath{\gamma}}_{m}=1.95\ifmmode\pm\else\textpm\fi{}0.08$. The phase diagram as a function of impurity concentration and an estimate for the infinite-lattice percolation limit are also given.

Real-space renormalization and the Baxter–Wu model

The lower-bound renormalization group approximation developed by Kadanoff and co-workers is modified by the introduction of a novel form of the weight function which preserves the ground states of the Baxter–Wu model. The approximation is applied to this model and the problems encountered are discussed together with the implications of this approach for other real-space approximations. The relevant exponents (exact) obtained are 1.363 (1.50) and 1.879 (1.875) and the critical coupling KC31 is 0.4558 (0.4407).

Modified critical behavior and crossover in the site impure Baxter-Wu model

A Monte Carlo technique has been used to study the critical behavior of the Baxter-Wu model containing random, quenched, non-magnetic impurities. The data indicate the appearance of new critical exponents due to the presence of the impurities.