Finite-size scaling and conformal anomaly of the Ising model in curved space

Details Finite-size scaling and conformal anomaly of the Ising model in curved space Finite-size scaling and conformal anomaly of the Ising model in curved space

1999-12-02

arxiv.org/abs/cond-mat/9912029v1

Phys.Rev. E61 (2000) 3384-3387

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 Postscript figures

Scientific paper

10.1103/PhysRevE.61.3384

We study the finite-size scaling of the free energy of the Ising model on lattices with the topology of the tetrahedron and the octahedron. Our construction allows to perform changes in the length scale of the model without altering the distribution of the curvature in the space. We show that the subleading contribution to the free energy follows a logarithmic dependence, in agreement with the conformal field theory prediction. The conformal anomaly is given by the sum of the contributions computed at each of the conical singularities of the space, except when perfect order of the spins is precluded by frustration in the model.

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