Benford's law detects quantum phase transitions similarly as earthquakes

Continuous Quantum Phase Transitions

A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite temperature counterparts, their dynamic and static critical behaviors are intimately intertwined. We show that considerable insight is gained by considering t...

Quantum Phase Transitions

whereM is a real, symmetric, positive-definite matrix (i.e. all eigenvalues are positive). This identity can be easily established by changing variables of integration to a basis in which M is diagonal. We will use this identity to compute the free energy density F , defined by Z = exp(−V F ) where V is the volume of spacetime. In the paramagnetic phase, r > 0, the perturbative expansion for F ...

Quantum Phase Transitions Go

U nderstanding matter—a collection of many interacting constituents, such as atoms and electrons—is a major endeavor in physics. While most studies in this field have focused on matter that is in thermal equilibrium with its environment, many phenomena occurring in nature involve matter out of equilibrium. The reason for this disparity may lie in the often-repeated observation that, to paraphra...

Quantum Phase Transitions - Lec

Quantum Phase Transitions