Geometric Critical Exponents in Classical and Quantum Phase Transitions
Statistical Mechanics
2015-06-19 v3 High Energy Physics - Theory
Abstract
We define geometric critical exponents for systems that undergo continuous second order classical and quantum phase transitions. These relate scalar quantities on the information theoretic parameter manifolds of such systems, near criticality. We calculate these exponents by approximating the metric and thereby solving geodesic equations analytically, near curvature singularities of two dimensional parameter manifolds. The critical exponents are seen to be the same for both classical and quantum systems that we consider, and we provide evidence about the possible universality of our results.
Cite
@article{arxiv.1405.3212,
title = {Geometric Critical Exponents in Classical and Quantum Phase Transitions},
author = {Prashant Kumar and Tapobrata Sarkar},
journal= {arXiv preprint arXiv:1405.3212},
year = {2015}
}
Comments
1 + 15 pages, LaTeX. Expanded version with several new examples added. Main results and conclusions are unchanged. Version to appear in Phys. Rev. E