Are critical exponents multivalued or unique?

Abstract

The scaling law theories of the critical point phenomena, together with possible stability conditions at the critical point, allow a whole range of critical exponents in a 2-dimensional system but only two sets of exponents in a 3-dimensional system. In the 3-dimensional case the two sets explain the differences between the critical exponents in magnetic and ferroelectric transitions. It also seems possible to correlate the small differences between the exponents of liquid/gas and magnetic transitions. No set of exponents is allowed in a 1-dimensional case, corresponding to the absence of phase transitions in a 1-dimensional system with short range interactions.