Kumar Prashant, Mahapatra Subhash, Phukon Prabwal, Sarkar Tapobrata
Department of Physics, Indian Institute of Technology, Kanpur 208016, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 1):051117. doi: 10.1103/PhysRevE.86.051117. Epub 2012 Nov 16.
We study geodesics on the parameter manifold for systems exhibiting second order classical and quantum phase transitions. The coupled nonlinear geodesic equations are solved numerically for a variety of models which show such phase transitions in the thermodynamic limit. It is established that both in the classical as well as in the quantum cases, geodesics are confined to a single phase and exhibit turning behavior near critical points. Our results are indicative of a geometric universality in widely different physical systems.
我们研究了表现出二阶经典和量子相变的系统在参数流形上的测地线。对于在热力学极限下显示出此类相变的各种模型，数值求解了耦合的非线性测地线方程。结果表明，在经典情况和量子情况下，测地线都局限于单一相，并在临界点附近表现出转向行为。我们的结果表明在广泛不同的物理系统中存在几何普遍性。
