A rescaling argument is applied to systems with a highly degenerate ground state. It is suggested that these systems can exhibit a distinctive low-temperature phase in which correlations decay algebraically with distance. This behaviour seens to be permitted when the spatial dimensionality is sufficiently high, d>or=d c . In addition, we find at d c an infinite-order phase transition ( nu = infinity , alpha =- infinity ) occurring at non-zero temperature, and only paramagnetic behaviour at d<d c . Since our results arise from a one-parameter renormalisation-group viewpoint, they should be seen as suggestive rather than definitive.
The work of an earlier paper on the ground-state properties of a system of bosons interacting via a strong short-ranged repulsive potential and a weak long-ranged attractive potential is extended to nonzero temperatures. The technique of temperature-dependent Green's functions is employed. It is shown that with the same restrictions on the two-body potential as imposed in the case of the ground state, it is possible to calculate in a consistent fashion the leading low-temperature contributions to the various thermodynamic functions. The results provide support for Landau's point of view for treating the system at low temperatures as a collection of noninteracting quasiparticles. The isotherms of the system at the low temperatures considered indicate a first-order transition between a phase with a condensate and one without a condensate, and also the possibility, at higher temperatures, of three phases.
We study the geometric Uhlmann phase of mixed states at finite temperature in a system of two coupled spin-
21 particles driven by a magnetic field applied to one of the spins. In the parameter space of temperature and coupling, we show the emergence of two topological Uhlmann phase transitions when the magnetic field evolves around the equator, where a winding number can characterize each temperature range. For small couplings, the width of the temperature gap of the nontrivial phase is roughly the critical temperature
Tc of one-dimensional fermion systems with two-band Hamiltonians. The first phase transition in the low-temperature regime and small values of the coupling corresponds to the peak of the Schottky anomaly of the heat capacity, typical of a two-level system in solid-state physics involving the ground and first excited states. The second phase transition occurs at temperatures very close to the second maximum of the heat capacity associated with a multilevel system. We also derive analytical expressions for the thermal Uhlmann phase for both subsystems, showing that they exhibit phase transitions. In the driven subsystem, for minimal
g, a topological phase transition appears at
Tc again. However, for larger values of
g, the transitions occur at lower-temperature values, and they disappear when the coupling reaches a critical value
gc. The latter is not the case for the undriven subsystem, where at low temperatures, a single phase transition occurs at
gc. Nevertheless, as the temperature rises, we demonstrate the emergence of two phase transitions defining a coupling gap, where the phase is nontrivial and vanishes as the temperature reaches a critical value.