Relation between the two-dimensional self-avoiding walk and the Eden model

When the interface of a two-dimensional lattice gas is grown by an algorithm producing self-avoiding walks, some features of the Eden model appear. The scaling behavior of the widths and lengths of these interfaces and of their accessible perimeters are examined in several regions of the phase diagram. It is found that both the accessible perimeter and the interface behave like the Eden model below a critical point. Above this point, only the accessible perimeter behaves like the Eden model. The behavior in the critical region is suprisingly the same for the interface and its external perimeter but is different from the Eden model.     

Eden growth model for aggregation of charged particles

The stochastic Eden model of charged particles aggregation in two-dimensional systems is presented. This model is governed by the following two parameters: screening length of electrostatic interaction, , and short-range attraction energy, E. Different patterns of finite and infinite aggregates are observed. They are of the following morphology types: linear or linear with bending, worm-like, DBM (dense-branching morphology), DBM with nucleus, and compact Eden-like. The transition between the different modes of growth is studied and phase diagram of the growth structures is obtained in co-ordinates. The detailed aggregate structure analysis, including analysis of their scaling properties, is presented. The scheme of the internal inhomogeneous structure of aggregates is proposed. Received 2 September 1998 and Received in final form 15 January 1999     

Non-equilibrium wetting transition in a magnetic Eden model

Magnetic Eden clusters (Ausloos et al., Europhys. Lett. 24, 629 (1993)) with ferromagnetic interaction between nearest-neighbor spins are grown in a confined 2d-geometry with short range magnetic fields acting on the surfaces. The change of the growing interface curvature driven by the field and the temperature is identified as a non-equilibrium wetting transition and the corresponding phase diagram is evaluated. Received 27 March 2000     

The Martinelli-Parisi expansion for the non-linear sigma model

The Martinelli-Parisi expansion around the Migdal-Kadanoff transformation is computed to second order in the shift parameter for the non-linear sigma model on a triangular lattice. The computation is performed in a completely analytical way in the region of weak coupling which is the most crucial region for checking the goodness of the expansion. The value of the beta function improves definitely with respect to the zero- and first-order results, reducing to 13% the error with regard to the exact value of continuum perturbation theory.     

Four-loop perturbative expansion for the lattice N-vector model

We compute the four-loop contributions to the β-function and the anomalous dimension of the field for the O(N)-invariant N-vector model. These results are used to compute the second analytic corrections to the correlation length and the general spin-n susceptibility.     

Strong coupling expansion in the massive Thirring model

A strong coupling expansion of the Green functions in the massive Thirring model is formulated. Expressions obtained for the fundamental fermion mass and theβ function agree with the known qualitative features of these physical quantities.     

Application of the connected-moments expansion to the half-filled Hubbard model

Summary In this paper we have applied the method of connected-moments expansion to investigate the ground state of the half-filled Hubbard model for both the linear chain and the square lattice. The CMX series appear very unstable and give rather poor estimates of the ground-state energies. This seems to suggest that it does not provide a useful method for estimating ground-state energies of this model.     

Breakdown of the operator-product expansion in the 't Hooft model

We consider deep inelastic scattering in the 't Hooft model. Being solvable, this model allows us to directly compute the moments associated with the cross section at next-to-leading order in the 1/Q(2) expansion. We perform the same computation using the operator-product expansion. We find that all the terms match in both computations except for one in the hadronic side, which is proportional to a nonlocal operator. The basics of the result suggest that a similar phenomenon may occur in four dimensions in the large N(c) limit.     

Landau expansion for a metamagnetic model

We performed a detailed Landau expansion of the free energy for a metamagnetic model considering terms up to twelfth order. We obtained explicit expressions for the coefficients as a function of the temperature and the ratio between ferro- and antiferromagnetic interactions. We showed that a naive analysis based on the signs of these coefficients cannot always give us sufficient guarantee about the correctness of the phase diagram of the model. In these cases it is necessary to resort to the full expression of the free energy in order to characterize the nature of the phase transition. Received 28 November 2001     

非对称Anderson模型的重整微扰展开

利用Yamada微扰论结合重整微扰方法来计算非对称Anderson模型,得到了局域电子占据数、重整化因子、重整化的局域能级以及重整化参数关于裸参数的展开式.计算了局域电子态密度和低温杂质电导,还计算了磁场对它们的影响,这些结果适用于从弱耦合到强耦合的整个耦合强度区域.由于在哈密顿量中已经将局域能级进行了初步重整,采用的重整微扰方法比Hewson的重整微扰方法更适合于研究非对称Anderson模型. 关键词： 非对称Anderson模型 重整化 磁场