https://doi.org/10.1007/s10051-001-8684-3
Twist free energy
1
Laboratoire de Physique Théorique (Unité Mixte de Recherche 8549 du Centre National de la
Recherche Scientifique et de l'École Normale Supérieure) , École Normale Supérieure, 24 rue Lhomond 75231, Paris Cedex 05,
France
2
Service de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette, France
Corresponding author: a brezin@corto.lpt.ens.fr
Received:
11
June
2001
Published online: 15 December 2001
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 
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.
PACS: 64.60.-i – General studies of phase transitions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001
