Category: Critical phenomena

Multicanonical Simulations of the Tails of the Order-Parameter Distribution of the two-dimensional Ising Model

Post author By R Hilfer
Post date April 9, 2005

R. Hilfer, B. Biswal, H.G. Mattutis, W. Janke

Computer Physics Communications 169, 230 (2005)
https://doi.org/10.1016/j.cpc.2005.03.053

submitted on
Saturday, April 9, 2005

We report multicanonical Monte Carlo simulations of the tails of the order-parameter distribution of the two-dimensional Ising model for fixed boundary conditions. Clear numerical evidence for “fat” stretched exponential tails is found below the critical temperature, indicating the possible presence of fat tails at the critical temperature.

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Critical phenomena Lattice Models Statistical Physics

Multicanonical Monte-Carlo Study and Analysis of Tails for the Order-Parameter Distribution of the Two-Dimensional Ising Model

Post author By R Hilfer
Post date February 10, 2003

R. Hilfer, B. Biswal, H.G. Mattutis, W. Janke

Physical Review E 68, 046123 (2003)
https://doi.org/10.1103/PhysRevE.68.046123

submitted on
Monday, February 10, 2003

The tails of the critical order-parameter distribution of the two-dimensional Ising model are investigated through extensive multicanonical Monte Carlo simulations. Results for fixed boundary conditions are reported here, and compared with known results for periodic boundary conditions. Clear numerical evidence for ‘‘fat’’ stretched exponential tails exists below the critical temperature, indicating the possible presence of fat tails at the critical temperature. Our work suggests that the true order-parameter distribution at the critical temperature must be considered to be unknown at present.

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Critical phenomena Lattice Models Statistical Physics

Thermodynamic potentials for the infinite range Ising model with strong coupling

Post author By R Hilfer
Post date September 30, 2002

R. Hilfer

Physica A 320, 429 (2003)
https://doi.org/10.1016/S0378-4371(02)01585-6

submitted on
Monday, September 30, 2002

The specific Gibbs free energy has been calculated for the infinite range Ising model with fixed and finite interaction strength. The model shows a temperature driven first-order phase transition that differs from the infinite ranged Ising model with weak coupling. In the temperature-field phase diagram the strong coupling model shows a line of first-order phase transitions that does not end in a critical point.

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Critical phenomena Equilibrium Simulations

Phase Transitions in Dense Lipid Monolayers Grafted to a Surface: Monte Carlo Investigation of a Coarse-Grained Off-Lattice Model

Post author By R Hilfer
Post date April 12, 1996

F. M. Haas, R. Hilfer, K. Binder

The Journal of Physical Chemistry 100 (37), 15290-15300 (1996)
DOI: 10.1021/jp9610980

submitted on
Friday, April 12, 1996

Semiflexible amphiphilic molecules end-grafted at a flat surface are modeled by a bead-spring chain with stiff bond angle potentials. Constant density Monte Carlo simulations are performed varying temperature, density, and chain length of the molecules, whose effective monomers interact with Lennard-Jones potentials. For not too large densities and low temperatures the monolayer is in a quasi-two-dimensional crystalline state, characterized by uniform tilt of the (stretched) chains. Raising the temperature causes a second-order transition into a (still solid) phase with no tilt. For the first time, finite size scaling concepts are applied to a model of a surfactant monolayer, and it is found that the technique in this case again is useful to locate the transition more precisely. For comparison, also a one-dimensional version of the model is studied, and directions for future extensions of this modeling are discussed.

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Tags lipid layer

Critical phenomena Simulations

Continuum Monte Carlo Simulation at Constant Pressure of Stiff Chain Molecules at Surfaces

Post author By R Hilfer
Post date August 31, 1995

F. M. Haas, R. Hilfer

Journal of Chemical Physics 105, 3859 (1996)
https://doi.org/10.1063/1.472206

submitted on
Thursday, August 31, 1995

Continuum Monte-Carlo simulations at constant pressure are performed on short chain molecules at surfaces. The rodlike chains, consisting of seven effective monomers, are attached at one end to a flat twodimensional substrate. It is found that the model exhibits phases similar to the liquid condensed and liquid expanded phases of Langmuir monolayers. The model is investigated here for a wide range of pressures and temperatures using a special form of constant pressure simulation compatible with the symmetry breaking during tilting transitions in the liquid condensed phases. At low pressures the chains undergo a tilting transition exhibiting tilt directions towards nearest and also next nearest neighbours depending on temperature. At elevated temperatures and low pressure the film enters a fluidlike phase similar to the liquid expanded phase observed in experiment.

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Tags lipid layer

Critical phenomena Equilibrium Statistical Physics

Are Critical Finite Size Scaling Functions Calculable From Knowledge of an Appropriate Critical Exponent ?

Post author By ICP
Post date December 6, 1994

R. Hilfer, N.B.Wilding

J. Phys. A: Math. Gen. 28, L281 (1995)
10.1088/0305-4470/28/10/001

submitted on
Tuesday, December 6, 1994

Critical finite size scaling functions for the order parameter distribution of the two and three dimensional Ising model are investigated. Within a recently introduced classification theory of phase transitions the universal part of critical finite size scaling functions has been derived by employing a scaling limit which differs from the traditional finite size scaling limit. In this paper the analytical predictions are compared with Monte Carlo simulation results. We find good agreement between the analytical expression and the simulation results. The agreement is consistent with the possibility that the functional form of the critical finite size scaling function for the order parameter distribution is determined uniquely by only a few universal parameters, most notably the equation of state exponent.

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Tags Ising model, order parameter, scaling function

Critical phenomena Equilibrium Simulations Statistical Physics

Continuum Monte-Carlo Simulations of Phase Transitions in Rodlike Molecules at Surfaces

Post author By R Hilfer
Post date October 28, 1994

R. Hilfer, F.M. Haas, K. Binder

Il Nuovo Cimento D 16, 1297-1303 (1994)
https://doi.org/10.1007/BF02458816

submitted on
Friday, October 28, 1994

Stiff rod-like chain molecules with harmonic bond length potentials and trigonometric bond angle potentials are used to model Langmuir monolayers at high densities. One end of the rod-like molecules is strongly bound to a flat two-dimensional substrate which represents the air-water interface. A ground-state analysis is performed which suggests phase transitions between phases with and without collective uniform tilt. Large-scale off-lattice Monte Carlo simulations over a wide temperature range show in addition to the tilting transition the presence of a strongly constrained melting transition at high temperatures. The latter transition appears to be related to two-dimensional melting of the head group lattice. These findings show that the model contains both, two- and three-dimensional ergodicity breaking solidification transitions. We discuss our findings with respect to experiment.

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Tags lipid layer

Critical phenomena Equilibrium Simulations Statistical Physics

Layers of Semiflexible Chain Molecules Endgrafted at Interfaces: An Off-Lattice Monte Carlo Simulation

Post author By R Hilfer
Post date July 11, 1994

F.M. Haas, R. Hilfer, K. Binder

Journal of Chemical Physics 102, 2960-2969 (1995)
https://doi.org/10.1063/1.468604

submitted on
Monday, July 11, 1994

A coarse‐grained model for surfactant chain molecules at interfaces in the high density regime is studied using an off‐lattice Monte Carlo technique. The surfactant molecules are modeled as chains consisting of a small number (e.g., seven) of effective monomers. For the modeling of lipid monolayers, each effective monomer is thought to represent several CH2 groups of the alkane chain, but applications of the model to other polymers end grafted at solid surfaces also should be possible. The head segments are restricted to move in the adsorption plane, but otherwise do not differ from the effective monomers, which all interact with Lennard‐Jones potentials. Bond angle and bond length potentials take into account chain connectivity and chain stiffness. The advantage of this crude model is that its phase diagram can be studied in detail. Temperature scans show two phase transitions, a tilting transition at low temperatures between a tilted and an untilted phase, and a melting transition at high temperatures where the lattice of head groups loses its crystalline order.

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Tags lipid layer

Critical phenomena Equilibrium Statistical Physics

Thermodynamic Scaling Derived via Analytic Continuation from the Classification of Ehrenfest

Post author By R Hilfer
Post date April 2, 1991

R. Hilfer

Physica Scripta 44, 321 (1991)
10.1088/0031-8949/44/4/002

submitted on
Tuesday, April 2, 1991

Scaling of the free energy is derived from thermodynamic arguments. The free energy is found to obey a new generalized scaling form which contains standard scaling as a special case. Contrary to standard scaling the new scaling form permits also nonuniversal exponents. The results are obtained by analytic continuation from the classification scheme of Ehrenfest.

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Critical phenomena Disordered Systems Fractals Lattice Models Random Walks Renormalisation Stochastic Processes

Renormalisation on Symmetric Fractals

Post author By R Hilfer
Post date July 9, 1984

R. Hilfer, A. Blumen

J.Phys.A: Math. Gen. 17, L783 (1984)
https://doi.org/10.1088/0305-4470/17/14/011

submitted on
Monday, July 9, 1984

We introduce and investigate new classes of Sierpinski-type fractals. We determine their fractal and spectral dimensions using renormalisation procedures and, for particular classes, we give these dimensions in closed form. The spectral dimensions densely fill the interval [1,2], allowing us to choose flexibly models for applications.

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Tags Anomalous Diffusion, finitely ramified, Markov chain, post-critically finite, real space renormalization