糖心TV

Second-order phase transitions are classified according to the values of critical exponents. In the 1960^Òs, four famous scaling relations linking these exponents were discovered and these are of fundamental importance in statistical physics and related areas. In certain important circumstances the transitional behaviour is modified by so-called logarithmic corrections. These are subtle effects that cloud the leading terms, and characterize the system. Here it shown that these logarithmic terms are also inter-related, just as the leading terms are, and a set of new scaling relations for them is presented. Consequently, a long-standing debate is automatically resolved. This concerns the Ising model in two dimensions, an old favourite for statistical physicists. Adding disorder to this system changes its critical behaviour but the precise nature of these changes has been under question. The new scaling relations relate hitherto elusive exponents characterizing these changes to well established ones in an unambiguous and precise fashion. This is one demonstration of how the new scaling relations are expected to become an important tool in modern statistical mechanics.