145 research outputs found
Structure of interfaces at phase coexistence : Theory and numerics
No full textWe compare results of the exact field theory of phase separation in two dimensions with Monte Carlo simulations for the q-state Potts model with boundary conditions producing an interfacial region separating two pure phases. We confirm in particular the theoretical predictions that below critical temperature the surplus of non-boundary colors appears in drops along a single interface, while for q > 4 at critical temperature there is formation of two interfaces enclosing a macroscopic disordered layer. These qualitatively different structures of the interfacial region can be discriminated through a measurement at a single point for different system sizes
Vortex Mass in the Three-Dimensional O(2) Scalar Theory
No full textWe study the spontaneously broken phase of the XY model in three dimensions, with boundary conditions enforcing the presence of a vortex line. Comparing Monte Carlo and field-theoretic determinations of the magnetization and energy density profiles, we numerically determine the mass of the vortex particle in the underlying O(2)-invariant quantum field theory. The result shows, in particular, that the obstruction posed by Derrick's theorem to the existence of stable topological particles in scalar theories in more than two dimensions does not in general persist beyond the classical level
Particles, string and interface in the three-dimensional Ising model
No full textWe consider the three-dimensional Ising model slightly below its critical temperature, with boundary conditions leading to the presence of an interface. We show how the interfacial properties can be deduced starting from the particle modes of the underlying field theory. The product of the surface tension and the correlation length yields the particle density along the string whose propagation spans the interface. We also determine the order parameter and energy density profiles across the interface, and show that they are in complete agreement with Monte Carlo simulations that we perform
Ambegaokar, Vinay: Reasoning about luck : probability and its uses in physics / Vinay Ambegaokar. - Cambridge [u.a.], 1996
No full textUntersuchungen zu uniaxial anisotropen Heisenberg-Antiferromagneten in zwei Dimensionen
No full textMotivated by recent experiments on cuprate antiferromagnets two-dimensional Ising and anisotropic Heisenberg models have been studied. Ising models with mobile and pinned defects are shown to describe the formation and thermal destruction of defect stripes. Modelling a specific "telephone number compound", a realistic Heisenberg model with randomly distributed, static defects reproduces nicely the experimental data on an anomaly in the susceptibility as a function of the external field. Moreover basic aspects of the phase diagrams of the XXZ antiferromagnet on a square lattice and variants have been analysed, using ground state considerations and Monte Carlo techniques. In particular the role of biconical structures and fluctuations in the classical version has been emphasised. For the quantum variant, the previously proposed scenario of a first-order transition between the antiferromagnetic and spin-flop phases has been scrutinised
Evidence for a bicritical point in the XXZ Heisenberg antiferromagnet on a simple cubic lattice
No full textGrundzustandseigenschaften von anisotropen antiferromagnetischen Heisenberg-Ketten mit Spin S = 1
No full textIn this thesis ground state properties of S = 1 spin chains with exchange and single-ion anisotropy are analysed. Following earlier publications two cases are mainly considered: A fixed ratio of the two anisotropies as well as a fixed and strong exchange anisotropy. The method primarily employed is the density matrix renormalization group (DMRG) for a finite chain length and in the thermodynamic limit (iDMRG). The phase diagrams of the quantum spin chain and the corresponding classical model are compared for the first time. Thereby the similarity of the phase diagrams, the correspondence of the phases and the striking differences are elucidated. The various phases of the quantum model include antiferromagnetic, ferromagnetic, spin liquid and supersolid phases. Their properties are discussed in detail. Analysing the correlation functions and using a correspondence to Luttinger liquids one can distinguish commensurate and incommensurate regions of the spin liquid phase. For different parameters the spin liquid phase may be subdivided into regions of ferroquadrupolar and spin-density-wave ordering. Some of the quantum phase transitions between the various phases are studied. Particularly the transition between the spin liquid and the supersolid phase is identified to be in the two-dimensional Ising universality class
Grundzustandseigenschaften von anisotropen antiferromagnetischen Heisenberg-Ketten mit Spin S = 1
No full textIn this thesis ground state properties of S = 1 spin chains with exchange and single-ion anisotropy are analysed. Following earlier publications two cases are mainly considered: A fixed ratio of the two anisotropies as well as a fixed and strong exchange anisotropy. The method primarily employed is the density matrix renormalization group (DMRG) for a finite chain length and in the thermodynamic limit (iDMRG). The phase diagrams of the quantum spin chain and the corresponding classical model are compared for the first time. Thereby the similarity of the phase diagrams, the correspondence of the phases and the striking differences are elucidated. The various phases of the quantum model include antiferromagnetic, ferromagnetic, spin liquid and supersolid phases. Their properties are discussed in detail. Analysing the correlation functions and using a correspondence to Luttinger liquids one can distinguish commensurate and incommensurate regions of the spin liquid phase. For different parameters the spin liquid phase may be subdivided into regions of ferroquadrupolar and spin-density-wave ordering. Some of the quantum phase transitions between the various phases are studied. Particularly the transition between the spin liquid and the supersolid phase is identified to be in the two-dimensional Ising universality class
Ambegaokar, Vinay: Reasoning about luck : probability and its uses in physics / Vinay Ambegaokar. - Cambridge [u.a.], 1996
No full textCritical Binder cumulant of two-dimensional Ising models
No full textThe fourth-order cumulant of the magnetization, the Binder cumulant,
is determined at the phase transition of
Ising models on square and triangular lattices, using Monte
Carlo techniques. Its value at
criticality depends sensitively on
boundary conditions, details of the
clusters used in calculating the cumulant, and symmetry of the
interactions or, here, lattice structure. Possibilities to
identify generic critical cumulants are discussed
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