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A new approach to critical phenomena in long-range models

Introductory Workshop: Probability and Statistics of Discrete Structures January 27, 2025 - January 31, 2025

January 30, 2025 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Tom Hutchcroft (California Institute of Technology)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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A new approach to critical phenomena in long-range models

Abstract

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Many statistical mechanics models on the lattice (including percolation, self-avoiding walk, the Ising model and so on) have natural "long-range" versions in which vertices interact not only with their neighbours, but with all other vertices in a way that decays with the distance. When this decay is described by a power-law, it can lead to new kinds of critical phenomena that are not present in the short-range models. In this talk I will describe a new approach to the study of these models, leading to some striking new results with surprisingly easy proofs.

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A new approach to critical phenomena in long-range models

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