Efficient parallel tempering for first-order phase transitions

We present a Monte Carlo algorithm that facilitates efficient parallel tempering simulations of the density of states $g\left(E\right)$. We show that the algorithm eliminates the supercritical slowing down in the case of the $Q=20$ and $Q=256$ Potts models in two dimensions, typical examples for systems with extreme first-order phase transitions. As recently predicted, and shown here, the microcanonical heat capacity along the calorimetric curve has negative values for finite systems.

Figure 1

Ergodicity autocorrelation times ${\tau }_{erg}$ in units of sweeps for $Q=256$ (circles) and $Q=20$ (triangles) as a function of $L$. The straight lines have slopes as given in Eq. (12)

Figure 2

Logarithmized energy distribution functions at ${\beta }_T$ for $L=8,9,\dots ,43,44$ at $Q=256$. Dashed curves belong to even values of L, solid ones to odd values.

Figure 3

Caloric specific heat $C_V\left(e\right)$ for the $Q=256$ Potts model on ${50}^2$ (circles), ${70}^2$ (tilted crosses), and ${90}^2$ lattices (squares) as a function of $e=E∕V$.