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1
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2D Falicov-Kimball Model in the Perturbative Regime at Finite Temperatures

100%
Dębski L.
Acta Physica Polonica A
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2009
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vol. 115
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issue 1
156-158
EN
Finite-temperature properties of the Falicov-Kimball model in two approximations were studied in the perturbative regime, i.e. for t/U ≪ 1, where t=1 is the hopping constant and U=10 denotes the Coulomb interaction strength. In our study, we determined the phase diagram of the model in the second order of the perturbation theory, where it reduces to the antiferromagnetic Ising model in the emergent magnetic field. In the fourth order, where our model constitutes the Ising model with more complicated frustrated antiferromagnetic interactions, the phase diagram was established. The Monte Carlo method was employed to investigate the phase transition lines. The existence of stripe ordering at finite temperatures is proved.
2
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Monte Carlo Simulations of the Ashkin-Teller Model

100%
Dębski L.
Acta Physica Polonica A
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2000
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vol. 97
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issue 5
859-862
EN
Monte Carlo simulations are used to analyse the behaviour of the extended Ashkin-Teller model in two (2D) and three (3D) dimensions from the ratio of the square of the second moment of the order parameter to its fourth moment. The critical surface in three dimensional parameter space is calculated in regions where the Ising transitions are expected both for the ferro-and antiferromagnetic regions.
3
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Application of Algebraic Combinatorics to Finite Spin Systems with Dihedral Symmetry

51%
Bucikiewicz S., Dębski L., Florek W.
Acta Physica Polonica A
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2001
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vol. 100
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issue 4
453-475
EN
Properties of a given symmetry group G are very important in investigation of a physical system invariant under its action. In the case of finite spin systems (magnetic rings as Fe_6, Cu_6, Fe_{10}, some planar macromolecules as Fe_{12} or Fe_8) the symmetry group is isomorphic with the dihedral group D_N. In this paper group-theoretical "parameters" of such groups are determined, especially decompositions of transitive representations into irreducible ones and double cosets. These results are necessary to construct matrix elements of any operator commuting with G in an efficient way. The approach proposed can be useful in many branches of physics, but here it is applied to finite spin systems, which serve as models for mesoscopic magnets.
4
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Quantum Effects and Critical Behavior in Low-Dimensional Spin-1/2 Systems

45%
Kamieniarz G., Musial G., Dębski L., Bieliński M., Dekeyser R.
Acta Physica Polonica A
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1997
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vol. 92
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issue 2
445-447
EN
The critical coupling and spontaneous magnetization curve for the 2D-Ising model are calculated using the effective-field method with correlations. An application of the method to the quantum S=1/2 1D-Heisenberg model is presented and reliable low-temperature estimates of the specific heat are evaluated.
5
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On Non-Ising Phase Transitions in the 3D Standard Ashkin-Teller Model

45%
Jeziorek-Knioła D., Musiał G., Dębski L., Rogiers J., Dylak S.
Acta Physica Polonica A
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2012
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vol. 121
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issue 5-6
1105-1107
EN
The phase transition line near the Ising point region is studied for the 3D standard Ashkin-Teller model on a cubic lattice. This model with a multicomponent order parameter is one of the important reference points in statistical physics since it shows an interesting and complicated phase diagram. The main motivation for our study was nonuniversal behavior suggested for this line. The large-scale Monte Carlo simulations using the Binder and Challa like cumulants are performed. Accurate analysis to exclude the latent heat inherence is applied. Specific behavior of the Challa like cumulants is discovered and its interpretation is proposed. The paper is closed with preliminary conclusions concerning the continuous but non-Ising character of these phase transitions in the lower part of the mixed phase region and the possiblity of the first order on the line connecting it to the Ising point.
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