Absence of mass gap for a class of stochastic contour models |
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Authors: | Alan D Sokal Lawrence E Thomas |
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Institution: | (1) Department of Physics, New York University, 10003 New York, New York;(2) Department of Mathematics, Pennsylvania State University, 16802 University Park, Pennsylvania;(3) Present address: Department of Mathematics, University of Virginia, 22903 Charlottesville, Virginia |
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Abstract: | We study a class of Markovian stochastic processes in which the state space is a space of lattice contours and the elementary motions are local deformations. We show, under suitable hypotheses on the jump rates, that the infinitesimal generator has zero mass gap. This result covers (among others) the BFACF dynamics for fixed-endpoint self-avoiding walks and the Sterling-Greensite dynamics for fixed-boundary self-avoiding surfaces. Our models also mimic the Glauber dynamics for the low-temperature Ising model. The proofs are based on two new general principles: the minimum hitting-time argument and the mean (or mean-exponential) hitting-time argument. |
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Keywords: | Markov chain Markov process contour model mass gap dynamic critical phenomena Monte Carlo Glauber dynamics self-avoiding walk |
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