Information geometry and phase transitions

Information Geometry and Phase Transitions

The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A noninteracting model has a flat geometry (R = 0), while R diverges at the critical point of an interacting one. Here, the information geometry is studied for a...

Geometry of Quasiminimal Phase Transitions

We consider the quasiminima of the energy functional Z Ω A(x,∇u) + F (x, u) dx , where A(x,∇u) ∼ |∇u| and F is a double-well potential. We show that the Lipschitz quasiminima, which satisfy an equipartition of energy condition, possess density estimates of Caffarelli-Cordoba-type, that is, roughly speaking, the complement of their interfaces occupies a positive density portion of balls of large...

The geometry of quantum phase transitions

Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions

A. T. Rezakhani,1,2 D. F. Abasto,2,3 D. A. Lidar,1,2,3,4 and P. Zanardi2,3 1Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA 2Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA 3Department of Physics, University of Southern California, Los Angeles, California 90089, USA 4Depar...

Geometry of dynamics, Lyapunov exponents and phase transitions

The Hamiltonian dynamics of classical planar Heisenberg model is numerically investigated in two and three dimensions. By considering the dynamics as a geodesic flow on a suitable Riemannian manifold, it is possible to analytically estimate the largest Lyapunov exponent in terms of some curvature fluctuations. The agreement between numerical and analytical values for Lyapunov exponents is very ...