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DY: Fachverband Dynamik und Statistische Physik
DY 23: Finite size effects at phase transitions III (session accompanying the symposium of the same name)
DY 23.3: Talk
Wednesday, March 28, 2007, 16:15–16:30, H3
Finite-size scaling study of the six-vertex F model on regular and random lattices — •Martin Weigel1 and Wolfhard Janke2 — 1Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK — 2Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany
Finite-size scaling (FSS) has been established as a powerful standard technique for
the analysis of phase transitions, in particular from numerical simulation data.
While in the common situation of a second (or even first) order phase transition, FSS
techniques easily lead to high-precision estimates, more care is needed in some
special circumstances such as the case of infinite-order
Berezinski-Kosterlitz-Thouless phase transitions, where the power laws are replaced
by exponentials and logarithmic corrections occur. We consider FSS in the
six-vertex F model representative of this universality class, using high-precision,
cluster-update Monte Carlo simulations [1]. The availability of an exact
solution for the thermodynamic limit of this model allows for a rather detailed
investigation of the occurring corrections. Extending on this, a further complication
is introduced by considering this model coupled to a class of random lattices with a
non-trivial fractal dimension, confining
the analysis to very small effective linear system sizes [2].
[1] M. Weigel and W. Janke, J. Phys. A 38 (2005) 7067.
[2] M. Weigel and W. Janke, Nucl. Phys. B 719 (2005) 312.