First-order transition in the one-dimensional three-state Potts model with long-range interactions

Abstract

The first-order phase transition in the three-state Potts model with long-range interactions decaying as 1/r 1+σ has been examined by numerical simulations using recently proposed Luijten-Blöte algorithm. By applying scaling arguments to the interface free energy, the Binder's fourth-order cumulant, and the specific heat maximum, the change in the character of the transition through variation of parameter σ was studied.

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“…In view of the expected behavior for nearestneighbor interactions, namely, F s scales to leading order as a power of the lattice size with an exponent given by the dimension of the interface [75], this suggests that the effective dimension of the interface lies between 0 and 1 for long-range chains. This assumption is also supported by the fact that the fits of F s /L in [69] exhibit important finite-size corrections, while our fit with a non-integer exponent does not suggest such corrections.…”

“…Infinite size temperatures are reported in Table V: the temperatures computed from both methods compare very well with each other and with the value of 1.691(3) reported in [7] using a multicanonical approach and medium lattice sizes. The value obtained from a previous MC study based on a canonical version of the Luijten-Blöte algorithm [69] lies clearly above our estimate, while estimates obtained from a transfer matrix method [70] and a real-space renormalization group approach [71] fall markedly below our values. Finally, the best estimate determined so far (to the best of our knowledge) with a numerical approach, namely, the value of T c = 1.68542 obtained in [72] with the cluster meanfield method, lies slightly below ours.…”

“…Our results in Fig. 12 show that the infinite size value lies around 1.033, and thus that the transition is stronger than suggested for instance in [69].…”

“…[70] 1.664 Ref. [69] 1.72 Ref. [71] 1.41 a crossover for both response functions led us to perform a distinct linear fit restricted to the three largest lattice sizes (see the inset of Fig.…”

Comment on “Potts Model with Long-Range Interactions in One Dimension”

“…[16] of [1]), (q 2,s 0.5) [4], and (q 3, s s c $ 0.65) [5]. This leads to the conclusion that the horizontal line q c 2 will in fact reach as far as s 0.5.…”