Physical Review Letters

First-Order Phase Transitions in Renormalization-Group Theory

Bernard Nienhuis, Michael Nauenberg

Published Aug 25, 1975• 328 citations

Abstract

Conditions are given for the renormalization-group transformations of the Hamiltonian of a thermodynamic system which lead to a discontinuity in an order parameter.Received 20 March 1975DOI:https://doi.org/10.1103/PhysRevLett.35.477©1975 American Physical Society

DOI: 10.1103/physrevlett.35.477

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Physical Review Letters

First-Order Phase Transitions in Renormalization-Group Theory

Bernard Nienhuis, Michael Nauenberg

Published Aug 25, 1975• 328 citations

Publisher

Abstract

DOI: 10.1103/physrevlett.35.477

Related papers

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Physical Review LettersAug 26, 19683 citations

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Hiroshi Matsuoka

For a system with a first or second order phase transition at ${\mathit{T}}^{\mathrm{*}}$ , we construct a type of renormalization group transformation that maps the reduced temperature t=(T- ${\mathit{T}}^{\mathrm{*}}$ )/ ${\mathit{T}}^{\mathrm{*}}$ and the external field h for a system of volume V to t\ensuremath{'} and h\ensuremath{'} for another system of volume V\ensuremath{'}. Our construction is purely thermodynamic without reference to effective Hamiltonians. Using the transformation, we derive the finite size scaling form for the singular part of the free energy, which leads to the scaling laws in the thermodynamic limit. We thus provide a unified thermodynamic framework for phase transitions. \textcopyright{} 1996 The American Physical Society.For a system with a first or second order phase transition at ${\mathit{T}}^{\mathrm{*}}$, we construct a type of renormalization group transformation that maps the reduced temperature t=(T-${\mathit{T}}^{\mathrm{*}}$)/${\mathit{T}}^{\mathrm{*}}$ and the external field h for a system of volume V to t\ensuremath{'} and h\ensuremath{'} for another system of volume V\ensuremath{'}. Our construction is purely thermodynamic without reference to effective Hamiltonians. Using the transformation, we derive the finite size scaling form for the singular part of the free energy, which leads to the scaling laws in the thermodynamic limit. We thus provide a unified thermodynamic framework for phase transitions. \textcopyright{} 1996 The American Physical Society.

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Physical Review LettersAug 18, 1975311 citations

For a system with a first or second order phase transition at

{\mathit{T}}^{\mathrm{*}}

, we construct a type of renormalization group transformation that maps the reduced temperature t=(T-

{\mathit{T}}^{\mathrm{*}}

{\mathit{T}}^{\mathrm{*}}

and the external field h for a system of volume V to t\ensuremath{'} and h\ensuremath{'} for another system of volume V\ensuremath{'}. Our construction is purely thermodynamic without reference to effective Hamiltonians. Using the transformation, we derive the finite size scaling form for the singular part of the free energy, which leads to the scaling laws in the thermodynamic limit. We thus provide a unified thermodynamic framework for phase transitions. \textcopyright{} 1996 The American Physical Society.