Salas, Jesús;
Sokal, Alan D;
(2022)
Ergodicity of the Wang–Swendsen–Kotecký algorithm on several classes of lattices on the torus.
Journal of Physics A: Mathematical and Theoretical
, 55
(41)
, Article 415004. 10.1088/1751-8121/ac92ae.
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Abstract
We prove the ergodicity of the Wang–Swendsen–Kotecký (WSK) algorithm for the zero-temperature q-state Potts antiferromagnet on several classes of lattices on the torus. In particular, the WSK algorithm is ergodic for q ⩾ 4 on any quadrangulation of the torus of girth ⩾ 4. It is also ergodic for q ⩾ 5 (resp. q ⩾ 3) on any Eulerian triangulation of the torus such that one sublattice consists of degree-4 vertices while the other two sublattices induce a quadrangulation of girth ⩾ 4 (resp. a bipartite quadrangulation) of the torus. These classes include many lattices of interest in statistical mechanics.
| Type: | Article |
|---|---|
| Title: | Ergodicity of the Wang–Swendsen–Kotecký algorithm on several classes of lattices on the torus |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/1751-8121/ac92ae |
| Publisher version: | http://dx.doi.org/10.1088/1751-8121/ac92a |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Eulerian triangulations, quadrangulations, torus, Kempe chains, antiferromagnetic Potts model, Wang–Swendsen–Kotecký algorithm, ergodicity |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10157142 |
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