Kumar Prashant, Sarkar Tapobrata
Department of Physics, Indian Institute of Technology, Kanpur 208016, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):042145. doi: 10.1103/PhysRevE.90.042145. Epub 2014 Oct 30.
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.
我们为经历连续二阶经典和量子相变的系统定义了几何临界指数。这些指数与此类系统在临界附近的信息理论参数流形上的标量相关。我们通过在二维参数流形的曲率奇点附近近似度量并由此解析求解测地线方程来计算这些指数。我们发现，对于我们所考虑的经典和量子系统，临界指数是相同的，并且我们提供了关于我们结果可能具有普适性的证据。
