Critical exponents in completely integrable models of quantum statistical physics

In one-dimensional quantum systems phase transition takes place at zero temperature. The general formula is obtained and investigated for the critical exponent describing the power decrease of zero-temperature correlators at long distances. This formula is valid for a great number of one-dimensional models including the Heisenberg model. The critical exponent is connected with fractional charge; it can also be expressed in terms of macroscopic characteristics of a model.