The study of liquid-liquid phase transitions has attracted considerable attention. One interesting example this phenomenon is phosphorus, for which the existence a first-order transition between low density insulating molecular and conducting polymeric been experimentally established. In Letter, we model by an ab initio quality dynamics simulation explore large portion liquid section diagram. W...

The deconfined quantum critical point (DQCP) between the N\'eel and valence bond solid order was originally proposed in spin systems with a local Hamiltonian. In last few years analogs of DQCPs nonlocal interactions have been explored, which can lead to rich possibilities. either arise from an instantaneous long-range interaction Hamiltonian, or gapless modes that reside one higher spatial dime...

It is known that the investigation of the critical point for models of the type of Dyson's hierarchical models is reduced to the solution of some non-linear integral equation. In our previous publication the Gaussian solution was investigated. Here we construct non-Gaussian solutions of the equation and find the expressions for critical indices connected with them. Our procedure permits us to c...

In this paper, we investigate the solutions of fourth-order discrete boundary value problem. By using critical point theory the existence of positive solutions and infinitely many solutions are obtained.

This paper is concerned with the existence of solutions to a boundary value problem of a fourth-order impulsive differential equation with a control parameter λ. By employing some existing critical point theorems, we find the range of the control parameter in which the boundary value problem admits at least one solution. It is also shown that under certain conditions there exists an interval of...