On the location of the 1-particle branch of the spectrum of the disordered stochastic Ising model

Michele Gianfelice; Marco Isopi

doi:10.3934/nhm.2011.6.127

Article Contents

2011, Volume 6, Issue 1: 127-144. Doi: 10.3934/nhm.2011.6.127

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On the location of the 1-particle branch of the spectrum of the disordered stochastic Ising model

Michele Gianfelice^1, and
Marco Isopi^2,

1.
Dipartimento di Matematica, Università della Calabria, Ponte Pietro Bucci, cubo 30B, 87036 Arcavacata di Rende
2.
Dipartimento di Matematica, "Sapienza" Università di Roma, Piazzale Aldo Moro 5, 00185 Roma

Received: October 31, 2009

Revised: October 31, 2010

Published: February 2011

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Abstract

We analyse the lower non trivial part of the spectrum of the generator of the Glauber dynamics for a $d$-dimensional nearest neighbour Ising model with a bounded random potential. We prove conjecture 1 in [1]: for sufficiently large values of the temperature, the first band of the spectrum of the generator of the process coincides with a closed non random segment of the real line.

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Mathematics Subject Classification: Primary: 82B44; Secondary: 60K35.

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References

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