Speaker
Description
The accurate determination of universal quantities, such as critical exponents,
by using high temperature series expansions or Monte Carlo simulations of
lattice models is hampered by corrections to scaling.
In [J. H. Chen, M. E. Fisher and B. G. Nickel, Phys. Rev. Lett. 48, 630 (1982)]
the authors suggested to study one parameter families of models.
The amplitudes of corrections to scaling depend on the parameter of the model
family. In the case of the Ising universality class in three dimensions a zero
of the amplitude of the leading correction can be found. Starting from the
nineties of the last century, this idea has been expoited by using Monte
Carlo simulations in conjunction with finite size scaling.
I sketch the basic ideas and summarize numerical results for the Ising, the
XY and the Heisenberg universality classes in three dimensions.
Recently I have studied the cubic fixed point in three dimensions. I obtain
y_t,cubic − y_t,O(3) = 0.00124(12) for the difference of the thermal
RG-exponents of the cubic and the O(3) invariant fixed points in three
dimensions.
