Absence of re-entrant phase transition of the antiferromagnetic Ising model on the simple cubic lattice: Monte Carlo study of the hard-sphere lattice gas

Physica A: Statistical Mechanics and its Applications

1995

Self Cite

Running title Critical phenomena of hard-sphere lattice gas Keywords Hard-sphere lattice gas, Critical phenomena, Monte Carlo method PACS classification codes 02.70.Lq, 64.60.Cn, 68.35.Rh AbstractWe study the critical phenomena of the hard-sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion by the Monte Carlo method. We get the critical exponents, β/ν = 0.313(9) and γ/ν = 2.37(2), where β is the critical exponent for the staggered density, γ for the staggered compressibility, and ν for the correlation length.

“…According to Meirovitch [13], we adopt the grand canonical ensemble. The algorithm is described in the references [13,14].…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

“…We start each simulation with a ground state configuration at the critical activity, z c = 1.0588 [14]. The pseudorandom numbers are generated by the Tausworthe method [26,27].…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Critical phenomena of the hard-sphere lattice gas on the simple cubic lattice

Physica A: Statistical Mechanics and its Applications

1995

Self Cite

“…According to Meirovitch [14], we adopt the grand canonical ensemble. The algorithm is described in the references [14,17].…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

“…For phase transitions and critical phenomena of a hard-sphere lattice gas [1,2,3] while many authors have investigated two-dimensional systems [4,5,6,7,8,9,10,11,12,13,14,15,16], there are only a few studies in three dimensions [8,17,18]. One of the reason is that series expansions or transfer matrix methods have been applied to the systems mainly.…”

Section: Introductionmentioning

confidence: 99%

Critical activity of the hard-sphere lattice gas on the body-centred cubic lattice

Physica A: Statistical Mechanics and its Applications

1996

Self Cite

Running title Critical activity of hard-sphere lattice gas Abstract This is the first Monte Carlo study of the hard-sphere lattice gas with nearest neighbour exclusion on the body-centred cubic lattice. We estimate the critical activity to be 0.7223 ± 0.0003. This result confirms that there is a re-entrant phase transition of an antiferromagnetic Ising model in an external field and a Blume-Emery-Griffiths model on the body-centred cubic lattice.

Universality in the three-dimensional hard-sphere lattice gas

Physica A: Statistical Mechanics and its Applications

1996

Self Cite

Abstract.We perform Monte Carlo simulations of the hard-sphere lattice gas on the body-centred cubic lattice with nearest neighbour exclusion. We get the critical exponents, β/ν = 0.311(8) and γ/ν = 2.38(2), where β, γ, and ν are the critical exponents of the staggered density, the staggered compressibility, and the correlation length, respectively. The values of the hard-sphere lattice gas on the simple cubic lattice agree with them but those of the threedimensional Ising model do not. This supports that the hard-sphere lattice gas does not fall into the Ising universality class in three dimensions.In this letter we study the hard-sphere lattice gas whose atoms interact with infinite repulsion of nearest neighbour pairs. The grand partition function iswhere z is an activity and Z V (N) is the number of configurations in which there are N atoms in the lattice of V sites. There are many studies on: the square lattice [1,2,3,4,5,6,7,8,9,10,11,12,13], the triangular lattice [3,6,9,10,14,15,16], the honeycomb lattice [17], the simple cubic lattice [1,3,9,14,18,19], the body-centred cubic lattice [3,9,14,20], and the face-centred cubic lattice [3]. On the simple cubic lattice the author has estimated the critical exponents, β/ν = 0.313(9) and γ/ν = 2.37(2), where β, γ, and ν are the critical exponents of the staggered density, the staggered compressibility, and the correlation length, respectively [18]. The corresponding values of the Ising model are β/ν = 0.518(7) and γ/ν = 1.9828(57) [21]. It does not seem that the hard-sphere lattice gas falls into the Ising universality class in three dimensions. The purpose of this letter is to obtain another piece of evidence of that. We estimate the critical exponents of the hard-sphere lattice gas on the body-centred cubic lattice.We carry out Monte Carlo simulations [22,23] of the hard-sphere lattice gas (1) on the body-centred cubic lattice of V sites, where V = 2×L×L×L (L = 2 × n, n = 2, 3, . . . , 30), under fully periodic boundary conditions [11,18]. We measure the staggered density,and the staggered compressibility,where R = 2 (N A − N B )/V and N A (N B ) is the number of the atoms in the A (B)-sublattice. Each run is divided into ten or twelve blocks. · · · is an expectation in a block and · · · is one over blocks. All the simulations are done at the critical activity, z c = 0.7223, [20] over 12 × 10 5 Monte Carlo steps per site (MCS/site) or 10 × 10 5 MCS/site after discarding 5 × 10 4 MCS/site to attain equilibrium. We have checked that simulations from the ground state configuration (The atoms occupy all the sites of one sublattice and the other 1 is vacant.) and no atom one gave consistent results. The pseudorandom numbers are generated by the Tausworthe method [24,25].We estimate a critical exponent and an amplitude by using the finite-size scaling [26,27,28] Figure 2 shows the size dependence of χ †′ at z = z c . The solid line indicates 0.037L 2.38 . The values of the critical exponents are consistent with those of the hardsphere lattice gas on the simple cubic...