Limiting distributions in critical systems

Jean-Yves Fortin (Nancy Université)

We consider the limiting distributions for the order parameter of spin models where a critical regime exists. In the XY-model, the distribution of a correctly defined order parameter in the low-temperature regime is found to be universal, non-gaussian and independent of the temperature or critical exponents and system size. We can numerically show that in the two-dimensional Ising model, there is a critical region where we recover the same limiting distribution. Finally, we will consider the interesting case of the spherical model where the distribution can be computed exactly at the critical point in any dimension and compared with the previous models.