A Monte Carlo renormalisation group study of the two-dimensional discrete cubic model: a hint for superconformal invariance

Abstract

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.