Unconventional Continuous Phase Transition in a Three-Dimensional Dimer Model

Phase transitions occupy a central role in physics, due both to their experimental ubiquity and their fundamental conceptual importance. The explanation of universality at phase transitions was the great success of the theory formulated by Ginzburg and Landau, and extended through the renormalization group by Wilson. However, recent theoretical suggestions have challenged this point of view in certain situations. In this Letter we report the first large-scale simulations of a three-dimensional model proposed to be a candidate for requiring a description beyond the Landau-Ginzburg-Wilson framework: we study the phase transition from the dimer crystal to the Coulomb phase in the cubic dimer model. Our numerical results strongly indicate that the transition is continuous and is compatible with a tricritical universality class, at variance with previous proposals.

Figure 1

Left panel: Specific heat per site $C_v/N$ as function of temperature $T$ for different system sizes $L$. Top right panel: Zoom on the second peak. Bottom right panel: Scaling of the specific heat at $T_c^{C_v}=1.676$ as a function of system size $L$. The dotted line denotes a power-law fit for the 4 largest systems $L=48$, 64, 80, 96 (see text).

Figure 2

Stiffness $K^{-1}$ multiplied by $L$ [obtained from $⟨{\varphi }^2⟩$, see Eq. (2)] versus $T$ near the transition, for different system sizes $L$. Left inset: Stiffness $K^{-1}$ for the whole high-$T$ range for $L=32$. Right inset: Scaling of the derivative $Ld{K}^{-1}/dT$ versus $L$ in log-log scale for the estimated critical temperature $T_c^K=1.6745$. The dotted line denotes a power-law fit for the 4 largest systems.

Figure 3

Crossing of the columnar Binder cumulant $B$ as a function of $T$ near the transition point for different system sizes $L$. The sample $L=16$ is again out of scaling. Left inset: Columnar order parameter $m$ and stiffness $K^{-1}$ (multiplied by 8) in the whole $T$ range for $L=32$. Right inset: Cumulant derivative $|dB/dT|$ at $T_c^{\mathrm{col}}=1.67525$ versus $L$ in log-log scale. The dotted line is a power-law fit for the 4 largest $L$.