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Conformal method of calculating critical indices in the theory of phase transitions

Efim S. Fradkin, M.Ya. Palchik, V. N. Zaikin

Published May 1, 1981• 0 citations
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Journal of Physics Conference Series•Nov 1, 2019•0 citations
The discrete cubic model for six states of the lattice variables is investigated at one special point of the phase diagram where a number of contradicting results are known concerning the order of the phase transition and the critical exponents. A new implementation of the MCRG method is used for determining the critical point with great accuracy and for calculating the critical exponents. A continuous phase transition is found. Following the recent results for six-state self-dual quantum chains with cubic symmetry where for a special point superconformal invariance is discovered, the critical exponents obtained are explained in the framework of this theory indicating a superconformal point with a conformal anomaly of c=1.25.
Abstract The thermodynamic properties and phase transitions in the two-dimensional weakly diluted Potts model with the number of spin states q=4 were studied by the Monte Carlo method. Systems with linear dimensions L×L = N, L=10–160 are considered. Using the fourth order Binder cumulant method, critical temperatures were calculated for spin systems with a spin concentration p=1.0 and 0.90. Critical indices are calculated on the basis of the theory of finite-size scaling. The universality of the critical behavior of two-dimensional disordered systems is discussed.