High-Temperature Series Expansions for Random Potts Models

We discuss recently generated high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. Using the star-graph expansion technique quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension d as symbolic parameters. We present analyses of the new series for the susceptibility of the Ising (q=2) and 4-state Potts model in three dimensions up to order 19 and 18, respectively, and compare our findings with results from field-theoretical renormalization group studies and Monte Carlo simulations.Comment: 16 pages,cmp209.sty (included), 9 postscript figures, author information under http://www.physik.uni-leipzig.de/index.php?id=2

High-Temperature series for the RPn−1RP^{n-1} lattice spin model (generalized Maier-Saupe model of nematic liquid crystals) in two space dimensions and with general spin dimensionality n

High temperature series expansions of the spin-spin correlation functions of the RP^{n-1} spin model on the square lattice are computed through order beta^{8} for general spin dimensionality n. Tables are reported for the expansion coefficients of the energy per site, the susceptibility and the second correlation moment.Comment: 6 pages, revtex, IFUM 419/FT, 2 figures not include

High Temperature Series Expansions for Spin- and Spin-Phonon-Systems

In this thesis the thermodynamical properties of spin- and spin-phonon-systems are investigated. In the first part of the thesis pure spin-1/2 models are addressed: the dimerized, frustrated chain, the ladder with cyclic exchange, and the two-dimensional Shastry-Sutherland model. The second part presents results for a spin-1/2 system coupled to lattice vibrations, i.e. phonons. By means of high temperature series expansions quantities like the magnetic susceptibility and the specific heat are calculated. These quantities are in most cases easily accessible experimentally. The obtained truncated series have the full dependence of the model parameters. Thus, fitting procedures become a fast and easy task. The coefficients of the truncated series are given as fractions of integers such that no accuracy is lost. The results are exact up to the given order. To improve the representations of the results extrapolation techniques are applied, namely Padé and Dlog-Padé extrapolations. The extrapolations are stabilized in the low temperature region using well-known information on the T=0 and on the low temperature behavior. The extrapolated series expansion results are gauged carefully by investigating their convergence and by comparing them to numerical data obtained from other methods like exact complete diagonalization, quantum Monte-Carlo, and transfer matrix-renormalization group. For the dimerized, frustrated spin system the difficulty is discussed to extract more than two coupling constants from the temperature dependence of the magnetic susceptibility. The ladder system is extended by the inclusion of a four-spin (cyclic) exchange. The impact of this new type of interaction is investigated. Comparison to experimental data of the ladder system SrCu2O3 shows, that the ladder model with a significant but small amount of cyclic exchange can serve as a description of the experimental data just as well as a pure ladder model. The inclusion of cyclic exchange leads to more realistic values for the coupling constants than the values obtained from fitting the ladder model without this type of exchange. The two-dimensional Shastry-Sutherland model has a realization in the compound SrCu2(BO3)2 allowing a detailed comparison between theory and experiment. The three-dimensionality of the substance is explicitly taken into account in the calculations using a mean-field like ansatz for the inter-layer coupling. The extrapolations of the high temperature series data can reproduce the experimental susceptibility data down to very low temperatures. The explicit calculations for the spin-1/2 system coupled to dispersionless phonons are performed using the cluster expansion technique. No cut-off in the phonon subspace is necessary such that the full phonon dynamics are taken into account. The influence of the additional coupling to the phononic degrees of freedom is addressed concerning the magnetic susceptibility and the specific heat

Updated tests of scaling and universality for the spin-spin correlations in the 2D and 3D spin-S Ising models using high-temperature expansions

We have extended, from order 12 through order 25, the high-temperature series expansions (in zero magnetic field) for the spin-spin correlations of the spin-S Ising models on the square, simple-cubic and body-centered-cubic lattices. On the basis of this large set of data, we confirm accurately the validity of the scaling and universality hypotheses by resuming several tests which involve the correlation function, its moments and the exponential or the second-moment correlation-lengths.Comment: 21 pages, 8 figure

Series expansions without diagrams

We discuss the use of recursive enumeration schemes to obtain low and high temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagramatic approaches and is easily generalizable. We illustrate the approach using the Ising model and generate low temperature series in up to five dimensions and high temperature series in three dimensions. The method is general and can be applied to any discrete model. We describe how it would work for Potts models.Comment: 24 pages, IASSNS-HEP-93/1

Phase diagrams of site diluted ferromagnetic semi infinite system

The spin correlations functions of face-centered cubic semi-infinite system are investigated by using the high  temperature series expansions extrapolated with the Padé approximant method for Heisenberg, XY and Ising models. The magnetic phase diagrams tc(n) versus the dilution x are obtained. The value obtained of the percolation threshold is. Xp≈0.2 The Xp is defined as the concentration at which tc =0The spin correlations functions of face-centered cubic semi-infinite system are investigated by using the high  temperature series expansions extrapolated with the Padé approximant method for Heisenberg, XY and Ising models. The magnetic phase diagrams tc(n) versus the dilution x are obtained. The value obtained of the percolation threshold is. Xp≈0.2 The Xp is defined as the concentration at which tc =

Random Exchange Quantum Heisenberg Chains

The one-dimensional quantum Heisenberg model with random $\pm J$ bonds is studied for $S=\frac{1}{2}$ and $S=1$. The specific heat and the zero-field susceptibility are calculated by using high-temperature series expansions and quantum transfer matrix method. The susceptibility shows a Curie-like temperature dependence at low temperatures as well as at high temperatures. The numerical results for the specific heat suggest that there are anomalously many low-lying excitations. The qualitative nature of these excitations is discussed based on the exact diagonalization of finite size systems.Comment: 13 pages, RevTex, 12 figures available on request ([email protected]

Phase diagrams of site diluted semi infinite ferromagnetic film

The magnetic susceptibility of a semi-infinite ferromagnetic films with a simple cubic lattice and the face centered cubic lattice is investigated by the method of exact high-temperature series expansions (HTSE) extrapolated with the Padé approximants method for Heisenberg, XY and Ising models. The magnetic phase diagrams in (tc (ν), c) plane are obtained. The value of the percolation threshold Xp is obtained. The Xp is defined at which tc= 0.The magnetic susceptibility of a semi-infinite ferromagnetic films with a simple cubic lattice and the face centered cubic lattice is investigated by the method of exact high-temperature series expansions (HTSE) extrapolated with the Padé approximants method for Heisenberg, XY and Ising models. The magnetic phase diagrams in (tc (ν), c) plane are obtained. The value of the percolation threshold Xp is obtained. The Xp is defined at which tc= 0

Phase diagrams of nanoparticles of diluted magnetic semiconductors

The magnetic properties of diluted magnetic semi conductors (DMS)Cd1-xMnxTe are investigated. Using the mean field theory, we have evaluated the critical temperature from the nearest neighbour interactions and the energy exchange for the different diameter of the Cd0.5Mn0.5Te nanoparticle. The critical exponents are obtained. The magnetic phase diagrams (Tc versus dilution ) have been determined by the High-temperature series expansions. The critical exponents associated with the magnetic susceptibility (g) and correlation lengths (v) are deduced.The magnetic properties of diluted magnetic semi conductors (DMS)Cd1-xMnxTe are investigated. Using the mean field theory, we have evaluated the critical temperature from the nearest neighbour interactions and the energy exchange for the different diameter of the Cd0.5Mn0.5Te nanoparticle. The critical exponents are obtained. The magnetic phase diagrams (Tc versus dilution ) have been determined by the High-temperature series expansions. The critical exponents associated with the magnetic susceptibility (g) and correlation lengths (v) are deduced