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Numerical tests of conjectures of conformal field theory for three-dimensional systems

M. Weigel·W. Janke
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Abstract

The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables, one thus obtains not only the critical exponents but even the corresponding amplitudes of the divergences analytically. A first numerical analysis brought up the question whether analogous results can be obtained for those systems on three-dimensional manifolds. Using Monte Carlo simulations based on the Wolff single-cluster update algorithm we investigate the scaling properties of O(n) symmetric classical spin models on a three-dimensional, hyper-cylindrical geometry with a toroidal cross-section considering both periodic and antiperiodic boundary conditions. Studying the correlation lengths of the Ising, the XY, and the Heisenberg model, we find strong evidence for a scaling relation analogous to the two-dimensional case, but in contrast here for the systems with antiperiodic boundary conditions.

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M. Weigel, W. Janke. 1999-04-07. Numerical tests of conjectures of conformal field theory for three-dimensional systems. https://doi.org/10.1002/(sici)1521-3889(199811)7%3A5%2F6%3C575%3A%3Aaid-andp575%3E3.0.co%3B2-m

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