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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01dv13zx56v
Title: The High Temperature 2D Ising Model: The Lee-Yang Gap is the Mass Gap
Authors: Borgnia, Noam
Advisors: Shapiro, Jacob
Department: Mathematics
Class Year: 2024
Abstract: The Lee-Yang circle theorem applied to the two-dimensional Ising model asserts that the pressure observable is a meromorphic function of the external magnetic field whose singularities lie along the imaginary axis. These singularities have been extensively classified in the low-temperature regime using Pirogov-Sinai Theory. In the high-temperature phase, for fixed temperatures arbitrarily close to the critical temperature, we attempt to establish an asymptotic correspondence between the radius of analyticity of the pressure observable (the Lee-Yang gap), and the rate of exponential decay for two-point correlations (the mass gap). In addition this report presents an exposition to the high temperature 2D Ising model with a focus on mapping the regime of exponential decay for two-point correlations using the Lebowitz Penrose theorem.
URI: http://arks.princeton.edu/ark:/88435/dsp01dv13zx56v
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Mathematics, 1934-2024

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