Scaling of thermal hysteresis with temperature scanning rate

We address several problems concerning thermal hysteresis and its characterization. Based on the time-dependent Ginzburg-Landau theory of the (Φ²{)}³$ model with O(N) symmetry in the large -N limit, we obtain numerically familiar spindle-shaped thermal hysteresis loops under linearly varying temperature. These hysteresis loops can be presented in the coordinate plane formed by the reduced temperature and its conjugate variable, so that the enclosed areas A of the loops represent directly the dissipation in the cycles. Moreover, this dissipation scales with the rate of temperature scanning R as A=A₀+aRⁿ, with n approaching two-thirds, universal for both the mean-field and field theoretical models concerned. The scaling results from the nature of the equilibrium transition point involved.