Rigorous studies of critical behavior

Michael Aizenman

doi:10.1016/0378-4371(86)90226-8

Rigorous studies of critical behavior

Michael Aizenman

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Presented here are some basic results on the phase structure and the critical behavior in general classes of translation invariant ferromagnetic systems, and in independent percolation models. Some of these results were derived by means of nonlinear partial differential inequalities involving the order parameter. While the inequalities are satisfied in the discrete lattice systems, their structure contains hints of relations with suitable field theories ("φ⁴" for ferromagnetic systems, and "φ³" in case of percolation).

Original language	English (US)
Pages (from-to)	225-231
Number of pages	7
Journal	Physica A: Statistical Mechanics and its Applications
Volume	140
Issue number	1-2
DOIs	https://doi.org/10.1016/0378-4371(86)90226-8
State	Published - Dec 1 1986
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Condensed Matter Physics

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10.1016/0378-4371(86)90226-8

Cite this

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abstract = "Presented here are some basic results on the phase structure and the critical behavior in general classes of translation invariant ferromagnetic systems, and in independent percolation models. Some of these results were derived by means of nonlinear partial differential inequalities involving the order parameter. While the inequalities are satisfied in the discrete lattice systems, their structure contains hints of relations with suitable field theories ({"}φ4{"} for ferromagnetic systems, and {"}φ3{"} in case of percolation).",

author = "Michael Aizenman",

note = "Funding Information: *Research supported in part by the NSF grant PHY-8605164 A02.",

year = "1986",

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doi = "10.1016/0378-4371(86)90226-8",

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Y1 - 1986/12/1

N2 - Presented here are some basic results on the phase structure and the critical behavior in general classes of translation invariant ferromagnetic systems, and in independent percolation models. Some of these results were derived by means of nonlinear partial differential inequalities involving the order parameter. While the inequalities are satisfied in the discrete lattice systems, their structure contains hints of relations with suitable field theories ("φ4" for ferromagnetic systems, and "φ3" in case of percolation).

AB - Presented here are some basic results on the phase structure and the critical behavior in general classes of translation invariant ferromagnetic systems, and in independent percolation models. Some of these results were derived by means of nonlinear partial differential inequalities involving the order parameter. While the inequalities are satisfied in the discrete lattice systems, their structure contains hints of relations with suitable field theories ("φ4" for ferromagnetic systems, and "φ3" in case of percolation).

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JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

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ER -

Rigorous studies of critical behavior

Abstract

All Science Journal Classification (ASJC) codes

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