Biomedical subjects

Wenan Guo

Publications and source records attributed to Wenan Guo.

6 recordsLinked to original sources

PubMed2006

Critical line of an n-component cubic model.

We consider a special case of the -component cubic model on the square lattice, for which an expansion exists in Ising-type graphs. We construct a transfer matrix and perform a finite-size-scaling analysis to determine the critical points for several values of . Furthermore we determine several universal quantities, including three critical exponents. For , these results agree well with the theoretical predictions for the critical branch. This model is also a special case of the model of Domany and Riedel. It appears that the self-dual plane of the latter model contains the exactly known critical points of the and 2 cubic models. For this reason we have checked whether this is also the case for . However, this possibility is excluded by our numerical results.

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PubMed2006

Exact characterization of O(n) tricriticality in two dimensions.

We propose exact expressions for the conformal anomaly and for three critical exponents of the tricritical O(n) loop model as a function of n in the range -2<or=n<or=3/2. These findings are based on an analogy with known relations between Potts and O(n) models and on an exact solution of a "tri-tricritical" Potts model described in the literature. We verify the exact expressions for the tricritical O(n) model by means of a finite-size scaling analysis based on numerical transfer-matrix calculations.

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PubMed2005

Percolation between vacancies in the two-dimensional Blume-Capel model.

Using suitable Monte Carlo methods and finite-size scaling, we investigate the Blume-Capel model on the square lattice. We construct percolation clusters by placing nearest-neighbor bonds between vacancies with a variable bond probability p(b) . At the tricritical point, we locate the percolation threshold of these vacancy clusters at p(bc) =0.706 33 (6) . At this point, we determine the fractal dimension of the vacancy clusters as Xf =0.1308 (5) approximately equal to 21/160, and the exponent governing the renormalization flow in the p(b) direction as y(p) =0.426 (2) approximately equal to 17/40 . For bond probability p(b) > p(bc) , the vacancy clusters maintain strong critical correlations; the fractal dimension is Xf =0.0750 (2) approximately equal to 3/40 and the leading correction exponent is y(p) =-0.45 (2) approximately equal to -19/40 . The above values fit well in the Kac table for the tricritical Ising model. These vacancy clusters have much analogy with those consisting of Ising spins of the same sign, although the associated quantities rho and magnetization m are energylike and magnetic quantities, respectively. However, along the critical line of the Blume-Capel model, the vacancies are more or less uniformly distributed over the whole lattice. In this case, no critical percolation correlations are observed in the vacancy clusters, at least in the physical region p(b) < or = 1 .

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PubMed2005

Monte Carlo renormalization: the triangular Ising model as a test case.

We test the performance of the Monte Carlo renormalization method in the context of the Ising model on a triangular lattice. We apply a block-spin transformation which allows for an adjustable parameter so that the transformation can be optimized. This optimization purportedly brings the fixed point of the transformation to a location where the corrections to scaling vanish. To this purpose we determine corrections to scaling of the triangular Ising model with nearest- and next-nearest-neighbor interactions by means of transfer-matrix calculations and finite-size scaling. We find that the leading correction to scaling just vanishes for the nearest-neighbor model. However, the fixed point of the commonly used majority-rule block-spin transformation appears to lie well away from the nearest-neighbor critical point. This raises the question whether the majority rule is suitable as a renormalization transformation, because the standard assumptions of real-space renormalization imply that corrections to scaling vanish at the fixed point. We avoid this inconsistency by means of the optimized transformation which shifts the fixed point back to the vicinity of the nearest-neighbor critical Hamiltonian. The results of the optimized transformation in terms of the Ising critical exponents are more accurate than those obtained with the majority rule.

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PubMed2002

Finite-size analysis of the hard-square lattice gas.

We investigate the hard-square lattice-gas model by means of transfer-matrix calculations and a finite-size-scaling analysis. Using a minimal set of assumptions we find that the spectrum of correction-to-scaling exponents is consistent with that of the exactly solved Ising model, and that the critical exponents and correlation-length amplitudes closely follow the relation predicted by conformal invariance. Assuming that these spectra are exactly identical, and conformal invariance, we determine the critical point, the conformal anomaly, and the temperature and magnetic exponents with numerical margins of 10(-11) or less. These results are in a perfect agreement with the exactly known Ising universal parameters in two dimensions. In order to obtain this degree of precision, we included system sizes as large as feasible, and used extended-precision floating-point arithmetic. The latter resource provided a substantial improvement of the analysis, despite the fact that it restricted the transfer-matrix calculations to finite sizes of at most 34 lattice units.

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PubMed2002

Phase transition in a two-dimensional Heisenberg model.

We investigate the two-dimensional classical Heisenberg model with a nonlinear nearest-neighbor interaction V(s,s') = 2K[(1+s x s')/2]p. The analogous nonlinear interaction for the XY model was introduced by Domany, Schick, and Swendsen, who find that for large p the Kosterlitz-Thouless transition is preempted by a first-order transition. Here we show that, whereas the standard (p = 1) Heisenberg model has no phase transition, for large enough p a first-order transition appears. Both phases have only short-range order, but with a correlation length that jumps at the transition.

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