Determine the finite-temperature transition behavior of lattice negative-coupling phi^4 theory

Determine whether the negative-coupling phi^4 theory on the lattice with parameters m_B^2a^2=0.5 and ga^2=0.05 exhibits a finite-temperature phase transition or rapid crossover by obtaining higher-resolution results on larger lattices.

Background

The paper studies finite-temperature observables of two-dimensional non-Hermitian phi4 theory with negative quartic coupling using a variational Hamiltonian method. At the lattice parameters m_B2a2=0.5 and ga2=0.05, the variational results for pressure and entropy density do not show a phase transition or rapid crossover, whereas the field expectation value changes gradually with temperature. The available lattice resolution is therefore insufficient to determine the finite-temperature phase structure, motivating calculations on larger lattices with higher resolution.

References

Taken as a whole, the lattice record for the finite-temperature properties with lattice parameters m_B2 a2=0.5, g a2=0.05 remains inconclusive. Pressure and entropy density in the variational method do not exhibit signs of a phase transition or rapid cross-over, even though the field expectation value \langle \phi\rangle does indicate a gradual change in behavior. Higher resolution on larger lattices would be a prerequisite to study the situation further.

— Variational Solution of Non-Hermitian Quantum Field Theory in Two Dimensions  (2609.19798 - Romatschke, 17 Sep 2026) in Section 3.4, "Finite Temperature"