Prof. David Sherrington FRS

Abstract:

We prove that the distribution functions of magnetization and spin glass order parameter coincide on the Nishimori line in the phase diagram of the +/-J Ising model in any dimension. This implies absence of replica symmetry breaking because the distribution function of magnetization consists only of two delta functions, suggesting the same simple structure for the distribution of the spin glass order parameter. It then follows that the mixed (glassy) phase, where ferromagnetic order coexists with a complex phase space structure, should lie below the Nishimori line if it exists at all. We also argue that the AT line that marks the onset of RSB with a continous distribution of the spin glass order parameter (again, if it exists) would start with an infinite slope from the multicritical point where paramagnetic, ferromagnetic and spin glass phases merge.

Abstract:

Recent results and interpretations are presented for the thermal minority game, concentrating on deriving and justifying the fundamental stochastic differential equation for the microdynamics.