Twist free energy |
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Authors: | E Brézin C De Dominicis |
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Institution: | (1) Laboratoire de Physique Théorique, école Normale Supérieure, 24 rue Lhomond 75231, Paris Cedex 05, France, FR;(2) Service de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette, France, FR |
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Abstract: | One may impose to a system with spontaneous broken symmetry, boundary conditions which correspond to different pure states
at two ends of a sample. For a discrete Ising-like broken symmetry, boundary conditions with opposite spins in two parallel
limiting planes, generate an interface and a cost in free energy per unit area of the interface. For continuum symmetries
the order parameter interpolates smoothly between the end planes carrying two different directions of the order parameter.
The cost in free energy is then proportional to Ld-2 for a system of characteristic size L. The power of L is related to the lower critical dimension, and the coefficient of this additional free energy vanishes at the critical temperature.
In this note it is shown within a loop expansion that one does find the expected behavior of this twist free energy. This
is a preamble to the study of situations where the broken continuum symmetry is believed to be more complex, as in Parisi
ansatz for the Edwards-Anderson spin glass.
Received 11 June 2001 |
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Keywords: | PACS 64 60 -i General studies of phase transitions |
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