# Equivalent-neighbor percolation models in two dimensions: Crossover between mean-field and short-range behavior

@article{Ouyang2018EquivalentneighborPM, title={Equivalent-neighbor percolation models in two dimensions: Crossover between mean-field and short-range behavior}, author={Yunqing Ouyang and Youjin Deng and Henk W. J. Blote}, journal={Physical Review E}, year={2018} }

We investigate the influence of the range of interactions in the two-dimensional bond percolation model, by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges, as expressed by the number $z$ of equivalent neighbors. We also consider the $z \to \infty$ limit, i.e., the complete graph case, where percolation bonds are allowed between each pair of sites, and the model becomes mean-field-like. All investigated models with finite $z$ are found to belong…

## 6 Citations

### Site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in two and three dimensions.

- PhysicsPhysical review. E
- 2022

Extended-range percolation on various regular lattices, including all 11 Archimedean lattices in two dimensions and the simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc)…

### Site and bond percolation on four-dimensional simple hypercubic lattices with extended neighborhoods

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

The asymptotic behavior of the percolation threshold p c and its dependence upon coordination number z is investigated for both site and bond percolation on four-dimensional lattices with compact…

### Bond percolation between k separated points on a square lattice.

- MathematicsPhysical review. E
- 2020

We consider a percolation process in which k points separated by a distance proportional the system size L simultaneously connect together (k>1), or a single point at the center of a system connects…

### Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit.

- PhysicsPhysical review. E
- 2021

By means of extensive Monte Carlo simulation, extended-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors up to the eighth nearest neighbors for the square lattice and the ninth nearestNeighborhoods are found using a single-cluster growth algorithm.

### Analysis of the Gel Point of Polymer Model Networks by Computer Simulations

- Computer Science
- 2020

The gel point of end-linked model networks is determined from computer simulation data. It is shown that the difference between the true gel point conversion, pc, and the ideal mean field predictio...

## References

SHOWING 1-10 OF 52 REFERENCES

### Theory of continuum percolation. II. Mean field theory.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

A previously introduced mapping between the continuum percolation model and the Potts fluid is used to derive a mean field theory of continuum perColation systems by introducing a new variational principle, which has to be taken, for now, as heuristic.

### Surface critical phenomena in three-dimensional percolation.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

Using Monte Carlo methods and finite-size scaling, this work investigates surface critical phenomena in the bond-percolation model on the simple-cubic lattice with two open surfaces in one direction and numerically derives the line of surface phase transitions occurring at pb < pbc.

### Dilute Potts model in two dimensions.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

The critical plane is found to contain a line of fixed points that divides into a critical branch and a tricritical one, just as predicted by the renormalization scenario formulated by Nienhuis et al for the dilute Potts model.

### Percolation in the canonical ensemble

- Physics
- 2012

We study the bond percolation problem under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We show via an analytical approach that at…

### Boundary between long-range and short-range critical behavior in systems with algebraic interactions.

- PhysicsPhysical review letters
- 2002

It is found that the boundary with short-range critical behavior occurs for interactions depending on distance r as r(-15/4), which answers a long-standing controversy between mutually conflicting renormalization-group analyses.

### Critical percolation clusters in seven dimensions and on a complete graph.

- MathematicsPhysical review. E
- 2018

It is demonstrated that the geometric structure of high-dimensional percolation clusters cannot be fully accounted for by their complete-graph counterparts.

### Medium-range interactions and crossover to classical critical behavior.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

We study the crossover from Ising-like to classical critical behavior as a function of the range R of interactions. The power-law dependence on R of several critical amplitudes is calculated from…

### Short-range correlations in percolation at criticality.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

It is found that at criticality, the connectivities depend on the linear finite size L as ∼L(yt-d), and the associated specific-heat-like quantities Cn and Cnn scale as ∼ L(2yt- d)ln(L/L0), where d is the lattice dimensionality, yt=1/ν the thermal renormalization exponent, and L0 a nonuniversal constant.

### Universal finite-size scaling for percolation theory in high dimensions

- Physics
- 2016

We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their…

### Crossover scaling in two dimensions

- Computer Science, Physics
- 1997

The data cover the full crossover region both above and below the critical temperature and support the hypothesis that the crossover functions are universal and the so-called effective exponents are discussed and it is shown that these can vary nonmonotonically in the crossover region.