Scaling corrections: site percolation and Ising model in three dimensions

Ballesteros, H. G.; Fernández, L.A.; Martı́n-Mayor, V.; Sudupe, A. Muñoz; Parisi, Giorgio; Ruiz‐Lorenzo, J. J.

doi:10.1088/0305-4470/32/1/004

Cited by 179 publications

(157 citation statements)

References 37 publications

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“…We also report the sequence γ (n) for the Ising model. If we extrapolate the results assuming a behavior of the form a + bn −∆ , with ∆ = 0.52, we obtain γ = 1.23857, 1.23832, 1.23801 using pairs n = (21, 23), (22,24), and (23,25). Clearly, the estimates converge towards the IA estimate γ = 1.2373(2).…”

Section: The Ratio Methodsmentioning

confidence: 70%

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice

et al. 2002

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25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In particular, we consider three improved potentials characterized by suppressed leading scaling corrections. Critical exponents are extracted from high-temperature series specialized to improved potentials, obtaining γ = 1.2373(2), ν = 0.63012(16), α = 0.1096(5), η = 0.03639(15), β = 0.32653(10), δ = 4.7893(8). Moreover, biased analyses of the 25th-order series of the standard Ising model provide the estimate ∆ = 0.52(3) for the exponent associated with the leading scaling corrections.By the same technique, we study the small-magnetization expansion of the Helmholtz free energy. The results are then applied to the construction of parametric representations of the critical equation of state, using a systematic approach based on a global stationarity condition. Accurate estimates of several universal amplitude ratios are also presented.

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Section: The Ratio Methodsmentioning

confidence: 70%

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice

et al. 2002

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“…For c > 0 we found also a sharp data collapse, but for a monotonically increasing exponent ν, which is for large c values compatible with the percolation critical exponent ν = 0.8765(16) on a three-dimensional simple cubic lattice. 23 One should keep in mind, however, that neither β 3D,c as extrapolated from the susceptibility peaks nor the estimate obtained from the crossing point in Fig. 5(a) is compatible with β c .…”

Section: Simulation and Resultsmentioning

confidence: 84%

Vortex-line percolation in the three-dimensional complex∣ψ∣4model

2005

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In discussing the phase transition of the three-dimensional complex |ψ| 4 theory, we study the geometrically defined vortex-loop network as well as the magnetic properties of the system in the vicinity of the critical point. Using high-precision Monte Carlo techniques we investigate if both of them exhibit the same critical behavior leading to the same critical exponents and hence to a consistent description of the phase transition. Different percolation observables are taken into account and compared with each other. We find that different connectivity definitions for constructing the vortex-loop network lead to different results in the thermodynamic limit, and the percolation thresholds do not coincide with the thermodynamic phase transition point.

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“…To extract critical exponents and critical temperatures, we have used the quotient methods: 18,19,35 for a pair of lattices of sizes L and 2L we choose the temperature where the correlation lengths in units of the lattice size coincide ͑2 L = 2L ͒. Up to scaling corrections, the matching temperature is the critical point.…”

Section: Monte Carlo Simulationmentioning

confidence: 99%

“…Let now O be a generic observable diverging at the critical point like ͉t͉ −x O . Then, one has ͑up to scaling corrections 18,19,35 …”

Section: Monte Carlo Simulationmentioning

confidence: 99%

Phase diagram of the bosonic double-exchange model

Alonso¹,

Cruz²,

Fernández³

et al. 2005

Phys. Rev. B

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The phase diagram of the simplest approximation to double-exchange systems, the bosonic double-exchange model with antiferromagnetic ͑AFM͒ superexchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions, and variational mean-field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segmentlike ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum ͑a cusp͒ in the specific heat. Below the phase transition, only short-range ordering would be found in neutron scattering. Researchers looking for a quantum critical point in manganites should be wary of this possibility. Finite-size scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.

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Scaling corrections: site percolation and Ising model in three dimensions

Cited by 179 publications

References 37 publications

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice

Vortex-line percolation in the three-dimensional complex∣ψ∣4model

Phase diagram of the bosonic double-exchange model

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