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Journal of Physics A Mathematical and General

Conformal invariance and the critical behaviour of a quantum spin Hamiltonian with three-spin coupling

Francisco Castilho Alcaraz, Michael N. Barber

Published Jan 11, 1987• 27 citations
Publisher

Abstract

A quantum spin model with three-spin coupling is studied by finite-lattice methods. The critical indices nu and alpha are obtained by standard finite-size scaling analysis. Conformal invariance is used to estimate the exponents nu and eta , the central charge or conformal anomaly c and the anomalous dimension of a spin 1/4 parafermion. The authors conclude that the model belongs to the same universality class as the four-state Potts and Baxter-Wu models, although the convergence of the various finite lattice estimators is extremely slow.

DOI
10.1088/0305-4470/20/1/026

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Journal of Statistical Mechanics Theory and Experiment•Oct 1, 2021•0 citations
A quantum spin model with three-spin coupling is studied by finite-lattice methods. The critical indices nu and alpha are obtained by standard finite-size scaling analysis. Conformal invariance is used to estimate the exponents nu and eta , the central charge or conformal anomaly c and the anomalous dimension of a spin 1/4 parafermion. The authors conclude that the model belongs to the same universality class as the four-state Potts and Baxter-Wu models, although the convergence of the various finite lattice estimators is extremely slow.
The ground-state properties of a quantum spin chain with three-spin couplings are investigated using finite-size calculations. The results are compared with the predictions of conformal invariance for finite systems at the critical point. The critical point. The critical exponents eta E and eta S of energy density and spin correlation functions are calculated and estimated to be eta E approximately=1.30 and eta S approximately=0.25. The results suggest that this model is conformally invariant with a central charge very close to or equal to one.
Finite-Size-Scaling and Conformal Invariance are used in order to find the phase diagram and critical exponents of a quantum spin chain with spin S=3/2S=3/2S=3/2. The model has a tetracritical point besides critical lines. The conformal anomaly and anomalous dimensions of some primary operators are calculated at the tetracritical point.
The phase diagram and the critical behavior of the spin-1 and the spin-3/2 two-dimensional Baxter-Wu model in a crystal field are studied by conventional finite-size scaling and conformal invariance theory. The phase diagram of this model, for the spin-1 case, is qualitatively the same as those of the diluted 4-states Potts model and the spin-1 Blume-Capel model. However, for the present case, instead of a tricritical point one has a pentacritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. On the other hand, for the spin-3/2 case, the phase diagram is much richer and can present, besides a pentacritical point, an additional multicritical end point. Our results also support that the universality class of the critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field is the same as the pure Baxter-Wu model, even at the multicritical points.
Abstract The scaling behaviour and conformal properties of a triangular Ising model with three-spin interactions at the critical point are studied using extensive Monte Carlo simulations. We show that in the continuum limit the external perimeter of spin clusters are conformally invariant and statistically equivalent to Schramm–Loewner evolution (SLE κ ) curves with diffusivity κ = 4, indicating that the loop ensembles associated with the critical Ising model with three-spin interactions, belonging to the universality class of domain walls in the four-states Potts model. The left-passage probabilities, distribution of the winding angle, and the driving function distribution for the interfaces are consistent with each other. We also study many geometrical properties of the critical interfaces to characterize the fractal structure and the other scaling properties of conformal loop ensembles. To this end, the fractal dimension of contours, the scaling properties of length and areas distributions and Zipf’s laws, are demonstrated numerically. Our results are compatible with the hyper-scaling relation for spin models.