Analysis of the Blume-Capel Model with the Wang-Landau Algorithm

Hurt, Daniel; Eitzel, M. A. I.; Scalettar, Richard; Batrouni, G. G.

doi:10.1007/978-3-540-32640-3_14

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“…Later, Xavier et al [9] considered the helical boundary conditions to calculate the conformal anomaly at the tricritical point with the estimation of the phase boundary. The nature of the phase transitions in the 2D BC model has been extensively examined also with various other numerical methods which include the Monte Carlo renormalization group [10,11], histogram method [12,13], Wang-Landau sampling [14][15][16][17][18][19], simulated * dongheekim@gist.ac.kr tempering [20], tensor renormalization group [21], replicaexchange Monte Carlo [22], and quite recently parallel multicanonical simulations [23]. While we focus on the pure BC model in this work, the effects of randomness have been also extensively studied [16,17,[24][25][26][27][28][29], where, for instance, the phase diagram was found to be shifted in presence of bond randomness at low temperatures [17].…”

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confidence: 99%

First-order transitions and thermodynamic properties in the 2D Blume-Capel model: the transfer-matrix method revisited

Jung

Kim

2017

Eur. Phys. J. B

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We investigate the first-order transition in the spin-1 two-dimensional Blume-Capel model in square lattices by revisiting the transfer-matrix method. With large strip widths increased up to the size of 18 sites, we construct the detailed phase coexistence curve which shows excellent quantitative agreement with the recent advanced Monte Carlo results. In the deep first-order area, we observe the exponential system-size scaling of the spectral gap of the transfer matrix from which linearly increasing interfacial tension is deduced with decreasing temperature. We find that the first-order signature at low temperatures is strongly pronounced with much suppressed finite-size influence in the examined thermodynamic properties of entropy, non-zero spin population, and specific heat. It turns out that the jump at the transition becomes increasingly sharp as it goes deep into the first-order area, which is in contrast to the Wang-Landau results where finite-size smoothing gets more severe at lower temperatures.

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