[HN Gopher] Magnetism Simulations: Three Months in Monte Carlo
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Magnetism Simulations: Three Months in Monte Carlo
Author : tempodox
Score : 72 points
Date : 2021-07-17 10:25 UTC (12 hours ago)
(HTM) web link (bit-player.org)
(TXT) w3m dump (bit-player.org)
| pops8 wrote:
| So...if things break down at high heat how is the earth producing
| its magnetic field? Do we have a frozen iron core?
| kadoban wrote:
| Good question. The article is only talking about so-called
| permanent magnets. Hunks of usually metal that exhibit this
| property under the right conditions.
|
| Sibling comment seems like it already covers the rest.
| _Microft wrote:
| Check this: https://en.wikipedia.org/wiki/Dynamo_theory
| bjornsing wrote:
| The author seems fascinated with the moving patterns produced by
| the M-rule but doesn't go into its similarity with Conway's game
| of life, and the fact that it's been proven Turing complete.
| dr_zoidberg wrote:
| I think it's been HN-hugged to death, so cached link:
| https://web.archive.org/web/20210717103315/http://bit-player...
|
| Edit: I glimpsed at it... it's long and full of details, plus the
| simulations run in the archived version!
| BenoitEssiambre wrote:
| That was amazing.
| sampo wrote:
| > How did the method get the name "Monte Carlo"?
|
| > The name, of course, is an allusion to the famous casino, a
| prodigious producer and consumer of randomness. Nicholas
| Metropolis claimed credit for coming up with the term. In a 1987
| retrospective he wrote: ...
|
| Here is the 1987 retrospective by N. Metropolis (6 pages):
|
| https://library.lanl.gov/cgi-bin/getfile?00326866.pdf
| honie wrote:
| I have only skimmed through the article but spent a bit of time
| on the "simultaneous update" part because it caught my eyes.
|
| If I'm not mistaken the author made a mistake in assuming that
| it's okay not modifying the spins in the first pass and then
| doing the update in the second pass, which would cause the system
| to approach a strange equilibrium with that flips between two
| states.
|
| For example, if you set the simulation temperature to well below
| that of the critical temperature of the system, a robust
| algorithm should eventually cause all of the spins align (to take
| the same sign).
|
| Also, and if I'm not mistaken, the author may have misunderstood
| that these simulations show the evolution of a system over time
| -- I think they are meant to show the possible states that a
| system can be in under a set of conditions, trying to rationalise
| whether or not it's sensible that spins should or shouldn't is
| perhaps not quite the right approach.
|
| The robustness of these algorithms are usually tested by
| carefully collecting many samples, and at different temperatures,
| and use them to estimate known properties of the systems. If an
| algorithm fails to estimate those quantities reasonably, then
| there is a good chance that it's not correctly implemented.
|
| If you're interested in this topic, one paper that I can
| immediately remember and is easy to read is this:
| https://arxiv.org/pdf/cond-mat/9703179.pdf. The section on Wolff
| algorithm, in particular, should solve the "mystery" of the
| simultaneous update. Here is a demo I have played with a few
| years ago that has the Wolff algorithm correctly implemented:
| https://mattbierbaum.github.io/ising.js (make sure you change
| sweep skip to an odd number for simulations at lower
| temperatures).
| [deleted]
| spekcular wrote:
| I have not read the article you linked, but the book by the
| same authors (Barkema and Newman, Monte Carlo Methods in
| Statistical Physics) is fantastic. It's the best introduction
| to these methods for the mathematically-minded that I've seen,
| in the sense that it gives quasi-rigorous justifications for a
| lot of claims, but at the same time doesn't get bogged down in
| rigor.
|
| They mention in the book that simultaneous updates with a
| checkboard are in fact OK. One just has to make the checkboard
| out of large squares of spins instead of the single spins the
| author of this article uses, and occasionally move the squares
| around to prevent boundary effects.
| comex wrote:
| > which would cause the system to approach a strange
| equilibrium with that flips between two states.
|
| The post explicitly mentions this kind of 'blinking' artifact
| and how it's problematic...
| mikewave wrote:
| Surprised to see an entire article about Ising model problems
| without any mention of the machines designed to solve them!
|
| This is exactly the kind of problems that the D-Wave quantum
| computers are designed to run, and in fact simulations of
| physical systems are one place where we've been able to
| demonstrate solid progress, e.g.
| https://science.sciencemag.org/content/361/6398/162 and several
| other papers.
|
| I'd highly encourage anyone interested in the Ising Hamiltonian
| and its uses for optimization problems to check out what we're
| doing and sign up for D-Wave Leap at www.dwavesys.com - we have
| demos, an in-browser IDE, Jupyter notebooks, a comprehensive
| Python SDK with excellent docs, and we'll give you free QPU time
| to run your problems in realtime on a quantum annealer.
| anniegarbage wrote:
| I recently had to read up on D-Wave for my job. Very cool stuff
| to an ex-computational-physicist.
| kgwgk wrote:
| As far as I can see it's about the Ising model and doesn't
| mention spin glasses at all.
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