On the fully anisotropic honeycomb lattice Green function, Bessel function integrals and Pearson random walks

2020 ◽  
Vol 53 (41) ◽  
pp. 415001
Author(s):  
G S Joyce
Keyword(s):  
Green Function ◽  
Random Walks ◽  
Bessel Function ◽  
Honeycomb Lattice

THE COMPENSATION BEHAVIOR AND INITIAL SUSCEPTIBILITIES OF A MIXED-SPIN HEISENBERG FERRIMAGNETIC SYSTEM IN AN EXTERNAL MAGNETIC FIELD

2007 ◽  
Vol 21 (07) ◽  
pp. 1077-1087 ◽  
Author(s):  
JUN LI ◽  
AN DU ◽  
GUOZHU WEI
Keyword(s):  
Magnetic Field ◽  
Magnetic Properties ◽  
Transition Temperature ◽  
External Magnetic Field ◽  
Green Function ◽  
Compensation Point ◽  
Function Technique ◽  
Honeycomb Lattice ◽  
Mixed Spin ◽  
Compensation Behavior

The magnetic properties of a mixed spin-2 and spin-5 / 2 Heisenberg ferrimagnetic system on a layered honeycomb lattice are investigated theoretically by a multisublattice Green-function technique which takes into account the quantum nature of Heisenberg spins. We calculate the magnetization and the compensation temperature and transition temperature of the system in an external magnetic field and in a zero external magnetic field, and find that the transition temperature of the system increases on the effect of an external magnetic field, the compensation point disappears when the single-ion anisotropy is not large and there are two compensation points when the anisotropy is large. We also calculate the initial susceptibilities of the system.

scholarly journals Algebraic area enumeration of random walks on the honeycomb lattice

2022 ◽  
Vol 105 (1) ◽  
Author(s):  
Li Gan ◽  
Stéphane Ouvry ◽  
Alexios P. Polychronakos
Keyword(s):  
Random Walks ◽  
Honeycomb Lattice

scholarly journals Local limit theorems in relatively hyperbolic groups I: rough estimates

2021 ◽  
pp. 1-41
Author(s):  
MATTHIEU DUSSAULE
Keyword(s):  
Green Function ◽  
Random Walks ◽  
Limit Theorems ◽  
Local Limit ◽  
Hyperbolic Groups ◽  
Relatively Hyperbolic Groups ◽  
The Green Function ◽  
Positive Recurrent ◽  
Relatively Hyperbolic ◽  
Local Limit Theorems

Abstract This is the first of a series of two papers dealing with local limit theorems in relatively hyperbolic groups. In this first paper, we prove rough estimates for the Green function. Along the way, we introduce the notion of relative automaticity which will be useful in both papers and we show that relatively hyperbolic groups are relatively automatic. We also define the notion of spectral positive recurrence for random walks on relatively hyperbolic groups. We then use our estimates for the Green function to prove that $p_n\asymp R^{-n}n^{-3/2}$ for spectrally positive-recurrent random walks, where $p_n$ is the probability of going back to the origin at time n and where R is the inverse of the spectral radius of the random walk.

Green function for the diffusion limit of one-dimensional continuous time random walks

2004 ◽  
Vol 114 (1-3) ◽  
pp. 165-171 ◽  
Author(s):  
W.T. Coffey ◽  
D.S.F. Crothers ◽  
D. Holland ◽  
S.V. Titov
Keyword(s):  
Green Function ◽  
Random Walks ◽  
Continuous Time ◽  
Diffusion Limit ◽  
One Dimensional ◽  
Continuous Time Random Walks

scholarly journals Gillis' Random Walks on Graphs

2005 ◽  
Vol 42 (1) ◽  
pp. 295-301 ◽  
Author(s):  
Nadine Guillotin-Plantard
Keyword(s):  
Random Walk ◽  
Green Function ◽  
Random Walks ◽  
Regular Graph ◽  
Simple Random Walk ◽  
Square Lattice ◽  
Random Walker ◽  
Unit Step ◽  
Random Walks On Graphs ◽  
The Green Function

We consider a random walker on a d-regular graph. Starting from a fixed vertex, the first step is a unit step in any one of the d directions, with common probability 1/d for each one. At any later step, the random walker moves in any one of the directions, with probability q for a reversal of direction and probability p for any other direction. This model was introduced and first studied by Gillis (1955), in the case when the graph is a d-dimensional square lattice. We prove that the Gillis random walk on a d-regular graph is recurrent if and only if the simple random walk on the graph is recurrent. The Green function of the Gillis random walk will be also given, in terms of that of the simple random walk.

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