Fighting topological freezing in the two-dimensional CPN−1 model

We perform Monte Carlo simulations of the CPN−1 model on the square lattice for N = 10, 21, and 41. Our focus is on the severe slowing down related to instantons. To fight this problem we employ open boundary conditions as proposed by Lüscher and Schaefer for lattice QCD. Furthermore we test the efficiency of parallel tempering of a line defect. Our results for open boundary conditions are consistent with the expectation that topological freezing is avoided, while autocorrelation times are still large. The results obtained with parallel tempering are encouraging.

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A two-dimensional diffusion model of the Venice lagoon and relative open boundary conditions

Ecological Modelling ◽

10.1016/0304-3800(87)90082-2 ◽

1987 ◽

Vol 37 (1-2) ◽

pp. 21-45 ◽

Cited By ~ 17

Author(s):

Camillo Dejak ◽

Ileana Mazzei Lalatta ◽

Ettore Messina ◽

Giovanni Pecenik

Keyword(s):

Boundary Conditions ◽

Diffusion Model ◽

Venice Lagoon ◽

Open Boundary ◽

Two Dimensional ◽

Open Boundary Conditions ◽

Dimensional Diffusion

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SUMMATION OF LOGARITHMIC INTERACTIONS IN PERIODIC MEDIA

International Journal of Modern Physics C ◽

10.1142/s0129183196000727 ◽

1996 ◽

Vol 07 (06) ◽

pp. 873-881 ◽

Cited By ~ 41

Author(s):

NIELS GRØNBECH-JENSEN

Keyword(s):

Monte Carlo ◽

Boundary Conditions ◽

Monte Carlo Simulations ◽

Periodic Boundary ◽

Periodic Boundary Conditions ◽

Dimensional System ◽

Two Dimensional ◽

Trigonometric Functions ◽

Periodic Media ◽

Two Dimensional System

We present a set of expressions for evaluating energies and forces between particles interacting logarithmically in a finite two-dimensional system with periodic boundary conditions. The formalism can be used for fast and accurate, dynamical or Monte Carlo, simulations of interacting line charges or interactions between point and line charges. The expressions are shown to converge to usual computer accuracy (~10–16) by adding only few terms in a single sum of standard trigonometric functions.

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Linear collapse of spatially linear, two-dimensional null points

Journal of Plasma Physics ◽

10.1017/s0022377802002003 ◽

2002 ◽

Vol 68 (3) ◽

pp. 221-235 ◽

Cited By ~ 4

Author(s):

C. MELLOR ◽

V. S. TITOV ◽

E. R. PRIEST

Keyword(s):

Steady State ◽

Boundary Conditions ◽

Plasma Flow ◽

Magnetic Force ◽

Open Boundary ◽

Two Dimensional ◽

Open Boundary Conditions ◽

Pressure Force ◽

Large Current ◽

Steady State Balance

A technique is developed for analysing the linear collapse properties of spatially linear two-dimensional null points with open boundary conditions. A treatment is given of the collapse of nulls which have current and flow so that they are initially in a steady-state balance between a magnetic force, a pressure force and a centrifugal force. This extends the previous results for initially current-free X-type nulls with no flow. It is found that all X-points, regardless of the current and flow tend to collapse. Also, O-points collapse in the absence of a plasma flow, but O-points with a large current and possessing a highly super-Alfvénic plasma flow can be stable against linear collapse.

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Phase transitions in free water nanoparticles. Theoretical modeling of [H2O]48 and [H2O]118

Physical Chemistry Chemical Physics ◽

10.1039/c4cp04909h ◽

2015 ◽

Vol 17 (16) ◽

pp. 10532-10537 ◽

Cited By ~ 3

Author(s):

Aleš Vítek ◽

René Kalus

Keyword(s):

Heat Capacity ◽

Monte Carlo ◽

Phase Transitions ◽

Monte Carlo Simulations ◽

Free Water ◽

Theoretical Modeling ◽

Parallel Tempering ◽

Two Dimensional ◽

Histogram Method

Classical parallel-tempering Monte Carlo simulations of [H2O]48 and [H2O]118 have been performed in the isothermal–isobaric ensemble and a two-dimensional multiple-histogram method has been used to calculate the heat capacity of the two clusters.

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Unphysical Frozen States in Monte Carlo Simulation of 2D Ising Model

International Journal of Modern Physics C ◽

10.1142/s0129183198000832 ◽

1998 ◽

Vol 09 (06) ◽

pp. 881-886 ◽

Cited By ~ 3

Author(s):

Andres R. R. Papa

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Ising Model ◽

Boundary Conditions ◽

Monte Carlo Simulations ◽

Periodic Boundary ◽

Random Access ◽

Periodic Boundary Conditions ◽

Two Dimensional ◽

Ising Systems

We show that for two-dimensional square Ising systems unphysical frozen states are obtained by just changing the instant of application of periodic boundary conditions during Monte Carlo simulations. The strange behavior is observed up to sample sizes currently used in literature. The anomalous results appear to be associated to the simultaneous use of type writer updating algorithms; they disappear when random access routines are implemented.

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