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MathGroup Archive 2000

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Re: ISING model

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23629] Re: ISING model
  • From: "Atul Sharma" <atulksharma at yahoo.com>
  • Date: Wed, 24 May 2000 02:16:32 -0400 (EDT)
  • Organization: McGill University
  • References: <8eg7v5$hgg@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I missed this post when it first appeared, as I was out of town. Apologies
if the response is too late to be of any use.

Richard Gaylord and Paul Wellin discuss the Ising spin model in their book:

Computer Simulations with Mathematica:
Explorations in Complex Physical and Biological Systems (Telos/Springer
Verlaag)

Chapter 6 deals implements the 'standard' Ising model with the Metropolis
algorithm. Chapter 10 implements the Q2R version of the model. The authors
describe the difference as

" The Q2R model is a CA version of the Ising model which was discussed in
Chapter 6. The two models differ in several significant ways. Q2R uses a
microcanonical ensemble approach while the Metropolis Ising model uses a
canonical ensemble approach. In Q2R, all of the spins are flipped
simultaneously while in the Metropolis model only one randomly selected spin
is flipped at a time. The spin-flipping decision is deterministic in Q2R
while it is probabilistic in the Metropolis model.Both versions of the Ising
model give many comparable results (though it should be pointed out that the
Q2R program is not exactly equivalent to Metropolis Ising program because
the CA is not ergodic) and we will not be concerned with those results
here."

In keeping with the practical orientation of the book, both chapters are a
bit short on theory, but they do have working implementations of the two
approaches.

Wolfgang Kinzel and Georg Reents (Physics by Computer: Programming Physical
Problems Using Mathematica and C ) have a more detailed discussion of the
theory. If  I recall correctly, the C routine for the Metropolis algorithm
runs externally under MathLink, which confers a significant speed gain. The
book is in my office, so my recall is sketchy. If you would like more detail
as to what it contains, feel free to write me off-list.

Bonne chance


Atul



-----------------------------------------------------------

Atul Sharma MD, FRCP(C)
Pediatric Nephrologist,
McGill University/Montreal Children's Hospital

Raphael Suire wrote in message <8eg7v5$hgg at smc.vnet.net>...
>
>Dear list,
>
>Help, i'am looking for a source for an ISING model
>
>Is anybody one know if there exist a source code for this kind of
> interacting particle system ????
>
>many thanks,
>
>Raphael Suire
>
>
>
>**********************************************************************
>Raphael Suire0
>CREREG - UMR CNRS 6585
>  0
>
>Faculte de Sciences Economiques
>7, place
>Hoche,
>CS86514
>35065 Rennes-France
>raphael.suire at univ-rennes1.fr
>*********************************************************************
>



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