  Thermal density matrices can be described by a pure quantum state within the
thermofield formalism. Here we show how to construct a class of Hamiltonians
realizing a thermofield state as their ground state. These Hamiltonians are
frustration-free, and can be Hermitian or non-Hermitian, allowing one to use
ground-state methods to understand the thermodynamic properties of the system.
In particular this approach gives an explicit mapping of thermal phase
transitions into quantum phase transitions. In the non-Hermitian case, the
quantum phase transition is not accompanied by a change in the spectrum of the
Hamiltonian, which remains gapped. We illustrate these ideas for the classical
2D Ising model.
