scholarly journals Three-dimensional universality class of the Ising model with power-law correlated critical disorder

2019 ◽  
Vol 100 (14) ◽  
Author(s):  
Wenlong Wang ◽  
Hannes Meier ◽  
Jack Lidmar ◽  
Mats Wallin
Keyword(s):  
Ising Model ◽  
Power Law ◽  
Three Dimensional ◽  
Universality Class

scholarly journals Critical flow and dissipation in a quasi–one-dimensional superfluid

2015 ◽  
Vol 1 (4) ◽  
pp. e1400222 ◽  
Author(s):  
Pierre-François Duc ◽  
Michel Savard ◽  
Matei Petrescu ◽  
Bernd Rosenow ◽  
Adrian Del Maestro ◽  
...  
Keyword(s):  
Power Law ◽  
Capillary Flow ◽  
Three Dimensional ◽  
Universality Class ◽  
Superfluid State ◽  
One Dimensional ◽  
Flow Experiment ◽  
20 Nm ◽  
Bulk Behavior ◽  
Superfluid Velocity

In one of the most celebrated examples of the theory of universal critical phenomena, the phase transition to the superfluid state of 4He belongs to the same three-dimensional (3D) O(2) universality class as the onset of ferromagnetism in a lattice of classical spins with XY symmetry. Below the transition, the superfluid density ρs and superfluid velocity vs increase as a power law of temperature described by a universal critical exponent that is constrained to be identical by scale invariance. As the dimensionality is reduced toward 1D, it is expected that enhanced thermal and quantum fluctuations preclude long-range order, thereby inhibiting superfluidity. We have measured the flow rate of liquid helium and deduced its superfluid velocity in a capillary flow experiment occurring in single 30-nm-long nanopores with radii ranging down from 20 to 3 nm. As the pore size is reduced toward the 1D limit, we observe the following: (i) a suppression of the pressure dependence of the superfluid velocity; (ii) a temperature dependence of vs that surprisingly can be well-fitted by a power law with a single exponent over a broad range of temperatures; and (iii) decreasing critical velocities as a function of decreasing radius for channel sizes below R ≃ 20 nm, in stark contrast with what is observed in micrometer-sized channels. We interpret these deviations from bulk behavior as signaling the crossover to a quasi-1D state, whereby the size of a critical topological defect is cut off by the channel radius.

Scaling Regimes and the Singularity of Specific Heat in the 3D Ising Model

2013 ◽  
Vol 14 (2) ◽  
pp. 355-369 ◽  
Author(s):  
J. Kaupužs ◽  
R. V. N. Melnik ◽  
J. Rimšāns
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Specific Heat ◽  
Power Law ◽  
Three Dimensional ◽  
The Other ◽  
Data Sets ◽  
Monte Carlo Data ◽  
Binder Cumulant ◽  
3D Ising Model

AbstractThe singularity of specific heat CV of the three-dimensional Ising model is studied based on Monte Carlo data for lattice sizes L≤1536. Fits of two data sets, one corresponding to certain value of the Binder cumulant and the other — to the maximum of CV, provide consistent values of C0 in the ansatz CV(L)=C0+ALα/ν at large L, if α/ν=0.196(6). However, a direct estimation from our data suggests that α/ν, most probably, has a smaller value (e.g., α/ν= 0.113(30)). Thus, the conventional power-law scaling ansatz can be questioned because of this inconsistency. We have found that the data are well described by certain logarithmic ansatz.

scholarly journals THE CLUSTER PROCESSOR: NEW RESULTS

1999 ◽  
Vol 10 (06) ◽  
pp. 1137-1148 ◽  
Author(s):  
HENK W. J. BLÖTE ◽  
LEV. N. SHCHUR ◽  
ANDREI L. TALAPOV
Keyword(s):  
Ising Model ◽  
Nearest Neighbor ◽  
Three Dimensional ◽  
Universality Class ◽  
Scaling Exponent ◽  
Monte Carlo Data ◽  
Correction To Scaling ◽  
Purpose Computer ◽  
Special Purpose Computer

We present a progress report on the Cluster Processor, a special-purpose computer system for the Wolff simulation of the three-dimensional Ising model, including an analysis of simulation results obtained thus far. These results allow, within narrow error margins, a determination of the parameters describing the phase transition of the simple-cubic Ising model and its universality class. For an improved determination of the correction-to-scaling exponent, we include Monte Carlo data for systems with nearest-neighbor and third-neighbor interactions in the analysis.

scholarly journals QUALITATIVE ASPECTS OF THE PHASE DIAGRAM OF J1–J2 MODEL ON THE CUBIC LATTICE

2013 ◽  
Vol 27 (26) ◽  
pp. 1350162 ◽  
Author(s):  
OCTAVIO D. R. SALMON ◽  
NUNO CROKIDAKIS ◽  
MINOS A. NETO ◽  
IGOR T. PADILHA ◽  
J. ROBERTO VIANA ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Ising Model ◽  
Effective Field Theory ◽  
Nearest Neighbor ◽  
Three Dimensional ◽  
Universality Class ◽  
Continuous Phase ◽  
Effective Field ◽  
Cubic Lattice ◽  
Plane Temperature

The qualitative aspects of the phase diagram of the Ising model on the cubic lattice, with ferromagnetic (F) nearest-neighbor interactions (J1) and antiferromagnetic (AF) next-nearest-neighbor couplings (J2) are analyzed in the plane temperature versus α, where α = J2/|J1| is the frustration parameter. We used the original Wang–Landau sampling (WLS) and the standard Metropolis algorithm to confront past results of this model obtained by the effective-field theory (EFT) for the cubic lattice. Our numerical results suggest that the predictions of the EFT are in general qualitatively correct, but the low-temperature re-entrant behavior, observed in the frontier separating the F and the collinear order, is an artifact of the EFT approach and should disappear when we consider Monte Carlo (MC) simulations of the model. In addition, our results indicate that the continuous phase transition between the F and the paramagnetic (P) phases, that occurs for 0.0 ≤α< 0.25, belongs to the universality class of the three-dimensional pure Ising Model.

PHASE TRANSTIONS IN THE 3-DIMENSIONAL 16-VERTEX MODEL

2001 ◽  
Vol 15 (24n25) ◽  
pp. 3331-3335 ◽  
Author(s):  
R. ADAM STERN ◽  
GEORGE F. TUTHILL
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Ising Model ◽  
Critical Behavior ◽  
Three Dimensional ◽  
Universality Class ◽  
Series Expansions ◽  
Vertex Model ◽  
3 Dimensional ◽  
Proton Ordering

A three-dimensional sixteen-vertex model on the diamond lattice describing proton ordering in KDP-type crystals is shown to exhibit both 1 st - and 2 nd -order phase transitions. The model's critical behavior was found, using analyses of series expansions and Monte Carlo simulations. When the transition is 2 nd -order, critical exponents belong to the universality class of the three-dimensional Ising model.

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