Phase Transitions in Low-Dimensional Systems and Renormalization Group Theory

I.A. Badrour, Rachid Aharrouch, N. Hachem +2 more

The spin-5/2 Blume–Capel model was studied using the mean-field approximation and the Migdal–Kadanoff renormalization group method for two- and three-dimensional systems. We determined the phase diagrams in the (crystal field, temperature) plane where the system exhibited first- and second-order phase transitions as well as isolated critical, bicritical and triple points. In order to show first-order transitions at low temperature, we presented the total magnetization per site and the derivative of the free energy as a function of the crystal field. Moreover, the critical exponents of the system were calculated by linearizing the renormalization transformation at the vicinity of the second-order fixed points.

Belal Ehsan Baaquie

Shinichiro Akiyama, Y. Kuramashi, Yusuke Yoshimura

We investigate the phase transition of the four-dimensional single-component ${\ensuremath{\phi}}^{4}$ theory on the lattice using the tensor renormalization group method. We have examined the hopping parameter dependence of the bond energy and the vacuum condensation of the scalar field $⟨\ensuremath{\phi}⟩$ at a finite quartic coupling $\ensuremath{\lambda}$ on large volumes up to $V=102{4}^{4}$ in order to detect the spontaneous breaking of the ${\mathbb{Z}}_{2}$ symmetry. Our results show that the system undergoes the weak first-order phase transition at a certain critical value of the hopping parameter. We also make a comparative study of the three-dimensional ${\ensuremath{\phi}}^{4}$ theory and find that the properties of the phase transition are consistent with the universality class of the three-dimensional Ising model.

Ivo Sachs, Siddhartha Sen, James Sexton

Adam Nahum, Kay Jörg Wiese

Field theoretic renormalization group is applied to measurement and entanglement phase transitions. The renormalization group flows for both random tensor networks and monitored systems show that, in high dimensions, there exist distinct weak- and strong-coupling universality classes for these phase transitions. In addition, one of the field theories exhibits a supersymmetry that leads to dimensional reduction by four.

Henry Fu