PERCOLATION OF INTERACTING DIFFUSING PARTICLES

被引:5
作者
SELINGER, RB [1 ]
STANLEY, HE [1 ]
机构
[1] BOSTON UNIV, DEPT PHYS, BOSTON, MA 02215 USA
来源
PHYSICAL REVIEW A | 1990年 / 42卷 / 08期
关键词
D O I
10.1103/PhysRevA.42.4845
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
We explore the connectivity properties of diffusing particles with short-range interactions for dimensions d=1,2. We consider both blind and myopic diffusion rules (for the blind case, the walker chooses the next step from among all neighbor sites while in the myopic case the walker chooses from among only the unblocked sites). We show that for all d the equilibrium state of a system of particles diffusing according to the blind rule, at density , is equivalent to the lattice gas with interaction parameter J=0 and chemical potential =2 sinh-1{[(2-1)2/4(1-)]1/2}. The connectivity properties of the blind diffusion system are described by random site percolation in all dimensions. The myopic diffusion system is more complicated. For d=1, the equilibrium state of a system of particles diffusing according to the myopic rule, with particle density , is equivalent to a lattice gas with J=-ln(2) and =ln(2)+2 sinh-1{[(2-1)2/2(1-)]1/2}. Also, for d=1, the number of clusters of size s is approximately ns=peffs-1(1-peff)2, where peff. An approximation for peff is given that agrees closely with Monte Carlo simulations. For d=2, the myopic diffusion system has no mapping to the lattice-gas model. Rather, it undergoes a percolation transition at a threshold density c. On the square lattice, c=0.6170.004, a value that is higher than the threshold for random site percolation. However, percolation and myopic diffusion appear to be in the same universality class. © 1990 The American Physical Society.
引用
收藏
页码:4845 / 4852
页数:8
相关论文
共 36 条
[1]   DIFFUSION OF INTERACTING PARTICLES ON FRACTAL AGGREGATES [J].
AMITRANO, C ;
BUNDE, A ;
STANLEY, HE .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1985, 18 (15) :L923-L929
[2]  
[Anonymous], 1971, CRITICAL PHENOMENA
[3]   MONTE-CARLO TESTS OF UNIVERSALITY IN A CORRELATED-SITE PERCOLATION PROBLEM [J].
BLUMBERG, RL ;
SHLIFER, G ;
STANLEY, HE .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1980, 13 (05) :L147-L152
[4]   DIFFUSION IN A STIRRED, PERCOLATING SYSTEM [J].
BUG, ALR ;
GEFEN, Y .
PHYSICAL REVIEW A, 1987, 35 (03) :1301-1310
[5]   ANOMALOUS TRAPPING - EFFECT OF INTERACTION BETWEEN DIFFUSING PARTICLES [J].
BUNDE, A ;
HAVLIN, S ;
NOSSAL, R ;
STANLEY, HE .
PHYSICAL REVIEW B, 1985, 32 (05) :3367-3369
[6]   Stochastic problems in physics and astronomy [J].
Chandrasekhar, S .
REVIEWS OF MODERN PHYSICS, 1943, 15 (01) :0001-0089
[7]   THERMAL PHASE-TRANSITION OF THE DILUTE S-STATE POTTS AND N-VECTOR MODELS AT THE PERCOLATION-THRESHOLD [J].
CONIGLIO, A .
PHYSICAL REVIEW LETTERS, 1981, 46 (04) :250-253
[8]   PERCOLATION PROBLEMS AND PHASE-TRANSITIONS [J].
CONIGLIO, A .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1975, 8 (11) :1773-1779
[9]   CLUSTERS AND ISING CRITICAL DROPLETS - A RENORMALIZATION GROUP-APPROACH [J].
CONIGLIO, A ;
KLEIN, W .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1980, 13 (08) :2775-2780
[10]   CLUSTERS AND ISING DROPLETS IN THE ANTI-FERROMAGNETIC LATTICE GAS [J].
CONIGLIO, A ;
DILIBERTO, F ;
MONROY, G ;
PERUGGI, F .
PHYSICS LETTERS A, 1982, 87 (04) :189-192