Dynamical phase transition of the long range anti-ferromagnets
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
About three decades ago, replica method was introduced to perform the average over quenched randomness of the spin glass models. After the success of this method, there appeared several suggestions which describe the glassy systems without quenched randomness by using replica method. In this presentation, we suggest the replica method based on the transformation common in replicas and study the low temperature phase of long range anti-ferromagnets(LRAF)1, especially the dynamical phase transition by imposing the marginally stable condition on the replica symmetry breaking solution, as suggested in 2.
LRAF is inspired by the following idea. Generally, some energy functions of glassy system are expressed as a summation of P constraint terms for N degrees of freedom,where P is the same order of N. This suggests to make an energy function by summing squared Fourier components made of spins, which is non-trivial for Ising spin and natually leads to LRAF. Actually, the high temperature expansion implies that there is a finite temperature where the entropy becomes zero, signaling the existence of phase transition. Applying replica method, we found the marginally stable solution, which is consistent with the results of simulated annealing.
Replica method we used is based on the transformation which are common in replicas. They do not change the overlap order parameters and replica partition function. This transformation works like quenched randomness of the usual replica method and give a non-trivial replicated action after summation. This idea seems quite general and we discuss some application to other glassy models. \\
1) Nokura K, J.Phys.A Math.Gen.35(2002) 4973\\
2) Marinari E, Parisi G, and Ritort F, J.Phys.A Math.Gen.27(1994)7615,7647