Relaxation to Equilibrium for Two Dimensional Disordered Ising Systems in the Griffiths Phase |
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Authors: | F Cesi C Maes F Martinelli |
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Institution: | Dipartimento di Fisica, Università“La Sapienza”, P.le A. Moro 2, 00185 Roma, Italy.?E-mail: cesi@vaxrom.roma1.infn.it, IT Instituut voor Theoretische Fysika, K.U. Leuven, Celestijnenlaan 200D, B-3001 Leuven and Onderzoeksleider N.F.W.O., Belgium. E-mail: Christian.Maes@fys.kuleuven.ac.be, BE Dipartimento di Energetica, Università dell' Aquila, Italy. E-mail: martin@mat.uniroma3.it, IT
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Abstract: | We consider Glauber–type dynamics for two dimensional disordered magnets of Ising type. We prove that, if the disorder–averaged
influence of the boundary condition is sufficiently small in the equilibrium system, then the corresponding Glauber dynamics is ergodic with probability one and the disorder–average C(t) of time–autocorrelation function satisfies (for large t). For the standard two dimensional dilute Ising ferromagnet with i.i.d. random nearest neighbor couplings taking the values
0 or J
0>0, our results apply even if the active bonds percolate and J
0 is larger than the critical value J
c
of the corresponding pure Ising model. For the same model we also prove that in the whole Griffiths' phase the previous upper
bound is optimal. This implies the existence
of a dynamical phase transition which occurs when J crosses J
c
.
Received: |
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Keywords: | |
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