arXiv subjects

K. D. Schotte

Publications and source records attributed to K. D. Schotte.

6 recordsLinked to original sources

arXiv2004

Canonical local algorithms for spin systems: Heat Bath and Hasting's methods

We introduce new fast canonical local algorithms for discrete and continuous spin systems. We show that for a broad selection of spin systems they compare favorably to the known ones except for the Ising +/-1 spins. The new procedures use discretization scheme and the necessary information have to be stored in computer memory before the simulation. The models for testing discrete spins are the Ising +/-1, the general Ising S or Blume-Capel model, the Potts and the clock models. The continuous spins we examine are the O(N) models, including the continuous Ising model (N=1), the ϕ^4 Ising model (N=1), the XY model (N=2), the Heisenberg model (N=3), the ϕ^4 Heisenberg model (N=3), the O(4) model with applications to the SU(2) lattice gauge theory, and the general O(N) vector spins with N\ge5.

cond-mat.stat-mech↗

arXiv2000

A Spin-1/2 Model for CsCuCl_3 in an External Magnetic Field

CsCuCl_3 is a ferromagnetically stacked triangular spin-1/2 antiferromagnet. We discuss models for its zero-temperature magnetization process. The models range from three antiferromagnetically coupled ferromagnetic chains to the full three-dimensional situation. The situation with spin-1/2 is treated by expansions around the Ising limit and exact diagonalization. Further, weak-coupling perturbation theory is used mainly for three coupled chains which are also investigated numerically using the density-matrix renormalization group technique. We find that already the three-chain model gives rise to the plateau-like feature at one third of the saturation magnetization which is observed in magnetization experiments on CsCuCl_3 for a magnetic field perpendicular to the crystal axis. For a magnetic field parallel to the crystal axis, a jump is observed in the experimental magnetization curve in the region of again about one third of the saturation magnetization. In contrast to earlier spinwave computations, we do not find any evidence for such a jump with the model in the appropriate parameter region.

cond-mat.str-el↗

arXiv2000

First and second order transition of frustrated Heisenberg spin systems

Starting from the hypothesis of a second order transition we have studied modifications of the original Heisenberg antiferromagnet on a stacked triangular lattice (STA-model) by the Monte Carlo technique. The change is a local constraint restricting the spins at the corners of selected triangles to add up to zero without stopping them from moving freely (STAR-model). We have studied also the closely related dihedral and trihedral models which can be classified as Stiefel models. We have found indications of a first order transition for all three modified models instead of a universal critical behavior. This is in accordance with the renormalization group investigations but disagrees with the Monte Carlo simulations of the original STA-model favoring a new universality class. For the corresponding x-y antiferromagnet studied before, the second order nature of the transition could also not be confirmed.

cond-mat.stat-mech↗

arXiv2000

First and second order transition in frustrated XY systems

The nature of the phase transition for the XY stacked triangular antiferromagnet (STA) is a controversial subject at present. The field theoretical renormalization group (RG) in three dimensions predicts a first order transition. This prediction disagrees with Monte Carlo (MC) simulations which favor a new universality class or a tricritical transition. We simulate by the Monte Carlo method two models derived from the STA by imposing the constraint of local rigidity which should have the same critical behavior as the original model. A strong first order transition is found. Following Zumbach we analyze the second order transition observed in MC studies as due to a fixed point in the complex plane. We review the experimental results in order to clarify the different critical behavior observed.

cond-mat.stat-mech↗

arXiv2000

Critical behavior of frustrated systems: Monte Carlo simulations versus Renormalization Group

We study the critical behavior of frustrated systems by means of Pade-Borel resummed three-loop renormalization-group expansions and numerical Monte Carlo simulations. Amazingly, for six-component spins where the transition is second order, both approaches disagree. This unusual situation is analyzed both from the point of view of the convergence of the resummed series and from the possible relevance of non perturbative effects.

cond-mat.stat-mech↗

arXiv1996

The L-Matrix for the Massive Thirring Model

As the new results for the massive Thirring model the L-matrix and the algebraic relations for its action angle variables are given. So it is shown most directly that this model which describes self-interacting relativistic Fermions in one-dimensional space is a quantum integrable system.

solv-int↗