Bounce solutions and the transition to thermal hopping in phi^4 theory   with a phi^3 term
  The nature of the transition from quantum tunneling at low temperatures to thermal hopping at high temperatures is investigated in a scalar field theory with cubic symmetry breaking. The bounce solution which interpolates between the zero-temperature and high-temperature solutions is obtained numerically, using a multigrid method. It is found that, for a small value of the symmetry-breaking coupling f, the transition is first-order. For higher values of f, the transition continues to be first-order, though weakly so. 
Hatem Widyan, A. Mukherjee, N. Panchapakesan and R. P. Saxena   (Department of Physics, University of Delhi, India)