Phase transition of four-dimensional lattice φ4 theory with tensor renormalization group

We investigate the phase transition of the four-dimensional single-component 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 at a finite quartic coupling lambda on large volumes up to V = 1024(4) in order to detect the spontaneous breaking of the 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 phi(4) theory and find that the properties of the phase transition are consistent with the universality class of the three-dimensional Ising model.

Automated summary

The study investigates the phase transition of the four-dimensional single-component φ(4) theory on the lattice using the tensor renormalization group method. It reveals that the system undergoes a weak first-order phase transition at a certain critical value of the hopping parameter, and comparative study with the three-dimensional φ(4) theory shows consistency with the universality class of the three-dimensional Ising model.