CLASSIFICATION-THEORY FOR PHASE-TRANSITIONS

A refined classification theory for phase transitions in thermodynamic s and statistical mechanics in terms of their orders is introduced and analyzed. The refined thermodynamic classification is based on two in dependent generalizations of Ehrenfests traditional classification sch eme. The statistical mechanical classification theory is based on gene ralized limit theorems for sums of random variables from probability t heory and the newly defined block ensemble limit. The block ensemble l imit-combines thermodynamic and scaling limits and is similar to the f inite size scaling limit. The statistical classification scheme allows for the first time a derivation of finite size scaling without renorm alization group methods. The classification distinguishes two fundamen tally different types of phase transitions. Phase transitions of order lambda > 1 correspond to well known equilibrium phase transitions, wh ile phase transitions with order lambda < 1 represent a new class of t ransitions termed anequilibrium transitions. The generalized order lam bda varies inversely with the strength of fluctuations. First order an d second order transitions play a special role in both classification schemes. First order transitions represent a limiting case separating equilibrium and anequilibrium transitions. The special role or second order transitions is shown to be related to the breakdown of hyperscal ing, For anequilibrium transitions the nature of the heat bath in the canonical ensemble becomes important.