tag:blogger.com,1999:blog-22973357.post8203333456404827882..comments2021-05-12T16:51:07.359-04:00Comments on Sabine Hossenfelder: Backreaction: Magnetism and the Ising ModelSabine Hossenfelderhttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comBlogger22125tag:blogger.com,1999:blog-22973357.post-66418173255446995942007-12-10T20:39:00.000-05:002007-12-10T20:39:00.000-05:00Hi Stefan and Thomas,Thanks for the new links [Pel...Hi Stefan and Thomas,<BR/><BR/>Thanks for the new links [Pelissetto et al] and updates RE Ising glass, lattice and models.<BR/><BR/>This Ising concept and phase transitions are really interesting.<BR/>They may be a type of information transition, rather than loss of magnetic information.<BR/>There may be some link to the Bekenstein and Hawking discussions of black hole information ~ a phase Doughttps://www.blogger.com/profile/07643919214761722345noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-78002394231471393892007-12-10T14:10:00.001-05:002007-12-10T14:10:00.001-05:00Hi Thomas,thanks for pointing out this review pape...Hi Thomas,<BR/><BR/>thanks for pointing out this review paper, I didn't know that. It's from after I've switched fields from magnetic phase transitions to heavy ions ;-)stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-47963876126835592292007-12-10T00:45:00.000-05:002007-12-10T00:45:00.000-05:00Doug,An Ising spin glass is related to, but not th...Doug,<BR/><BR/>An Ising spin glass is related to, but not the same as, the Ising model. There is a huge literature on spin glasses, but the little I once knew about it I have long forgotten.<BR/><BR/>But if you seriously want to study phase transition theory, the following Phys. Rep. probably contains everything you want to know (and a lot more):<BR/><BR/><A HREF="http://arxiv.org/abs/cond-mat/Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-69371597377779212562007-12-09T11:56:00.000-05:002007-12-09T11:56:00.000-05:00Hi doug,I have only been able to read the first 7,...Hi doug,<BR/><BR/><I>I have only been able to read the first 7, but hope to read the rest over the next year.</I><BR/><BR/>Sorry, the suggestion was serious, but I didn't want you to read all the papers, but maybe just have a look at the abstracts to get an impression about the issues that are looked at in connection with the 3D Ising model. I don't know anything about your background, so pleasestefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-17744284786134831432007-12-09T11:14:00.000-05:002007-12-09T11:14:00.000-05:00Hi Stefan and Thomas Larsson,1 - Thanks for the 70...Hi Stefan and Thomas Larsson,<BR/><BR/>1 - Thanks for the 70 arXiv references to the “3D Ising”<BR/>I have only been able to read the first 7, but hope to read the rest over the next year.<BR/><BR/>I have noticed two ideas:<BR/>a - Ref_7 S. Perez Gaviro, et al, ’Study of the phase transition in the 3d Ising spin glass from out of equilibrium numerical simulations’ suggests game theory to me. I Doughttps://www.blogger.com/profile/07643919214761722345noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-79470564318797305192007-12-08T17:54:00.000-05:002007-12-08T17:54:00.000-05:00I have managed to confuse myself thoroughly. Supp...I have managed to confuse myself thoroughly. Suppose we try drawing the cycle of Paul's engine on a temperature-entropy plot, what would it look like? <BR/><BR/>The fixed work per cycle means even as T(source) tends to T(sink) the area in this cycle remains fixed.<BR/><BR/><A HREF="http://en.wikipedia.org/wiki/Carnot_cycle" REL="nofollow">See Wiki diagram</A>Arunhttps://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-76177333876021762082007-12-06T20:50:00.000-05:002007-12-06T20:50:00.000-05:00Hi Thomas,thank you for collecting the links! It's...Hi Thomas,<BR/><BR/>thank you for collecting the links! It's impressive what is there already... and<BR/><BR/><BR/>Hi Paul,<BR/><BR/>about magnetic cooling, I have just found the Wikipedia entry on <A HREF="http://en.wikipedia.org/wiki/Magnetic_refrigeration" REL="nofollow">Magnetic refrigeration</A>... now, that's some stuff to start with... I'll have to digest all that a bit...<BR/><BR/>Best, stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-46377237254525122062007-12-06T02:50:00.000-05:002007-12-06T02:50:00.000-05:00Some refences on Wikipedia:Ken WilsonMike FisherLe...Some refences on Wikipedia:<BR/><A HREF="http://en.wikipedia.org/wiki/Kenneth_G._Wilson" REL="nofollow">Ken Wilson</A><BR/><A HREF="http://en.wikipedia.org/wiki/Michael_E._Fisher" REL="nofollow">Mike Fisher</A><BR/><A HREF="http://en.wikipedia.org/wiki/Leo_Kadanoff" REL="nofollow">Leo Kadanoff</A><BR/><A HREF="http://en.wikipedia.org/wiki/Phase_transition" REL="nofollow">phase transitions</A><BR/Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-37523464350653546392007-12-06T02:39:00.000-05:002007-12-06T02:39:00.000-05:00Like Stefan, I don't have any references handy, bu...Like Stefan, I don't have any references handy, but one place to start at is <A HREF="http://en.wikipedia.org/wiki/Ising_model" REL="nofollow">Wikipedia</A>.<BR/><BR/>One can only compute the partition function exactly in 1D and 2D, but some exact information is known in higher dimensions. In particular, the critical exponents when d >= 4 are correctly given by mean field theory. This follows Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-40793320561427658892007-12-05T21:56:00.000-05:002007-12-05T21:56:00.000-05:00Hi Stefan --I'm glad that you've found the heat en...Hi Stefan --<BR/><BR/>I'm glad that you've found the heat engine question interesting. I have to say that I don't think you'll resolve anything focussing on the question of whether the current/voltage needs to be rectified. Even if you assume a polarized DC load that can only do "useful" electrical work with the right polarity, this can easily be accommodated: (1) don't connect the coil to the Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-79115400989002172712007-12-05T12:21:00.000-05:002007-12-05T12:21:00.000-05:00Dear Arun,thank you for your comment! I'll have to...Dear Arun,<BR/><BR/>thank you for your comment! I'll have to give a second thought to Carnot cycles operating around a phase transition with latent heat... it's probably a typical textbook problem...<BR/><BR/>However, I am still confused about Paul's machine. As said before, if you look, for example, at the current induced in the coil when spontaneous magnetisation sets in when crossing the Curiestefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-65541842437570600552007-12-04T22:14:00.000-05:002007-12-04T22:14:00.000-05:00Dear Stefan,The paradox is that around a phase tra...Dear Stefan,<BR/><BR/>The paradox is that around a phase transition one can build an almost isothermal engine. However, per cycle, this engine seems to do a fixed amount of work (even if small), even as the source and sink temperatures become arbitrarily close.<BR/><BR/>Paul's device needs no diode or rachet. For example, it can be used for electrolysis of water. Yes, the H2 and 02 will be mixedArunhttps://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-90958440908978472982007-12-04T21:56:00.000-05:002007-12-04T21:56:00.000-05:00Hi Doug,thank you for the reference - I am not so ...Hi Doug,<BR/><BR/><BR/>thank you for the reference - I am not so familiar with this kind of stuff, it may be relevant to the Ising model, but I do not see it immediately.<BR/><BR/>But I am quite sure that you will be famous if you find an exact solution to the 3D Ising model ;-), at least among the physics geeks. I mean, exact solution says that you can write down a formula for the partition stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-70835156568357595032007-12-04T21:36:00.000-05:002007-12-04T21:36:00.000-05:00Hi Changcho,If I recall correctly from stat mech.,...Hi Changcho,<BR/><BR/><BR/><I>If I recall correctly from stat mech., originally Ising created his model assuming only 1 dimension, which has an exact solution.</I><BR/><BR/>yes, you recall nearly correctly ;-) - the model had been formulated by Lenz, who was Ising's PhD thesis advisor. In his thesis, Ising calculated the partition function for the restriction to 1D (that's an quite easy stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-32444359706550804422007-12-04T21:10:00.000-05:002007-12-04T21:10:00.000-05:00Hi Arun, Paul,I am still not sure if I have unders...Hi Arun, Paul,<BR/><BR/>I am still not sure if I have understood the idea correctly. <BR/><BR/>As I see it, this is not related to latent heat - many magnetic transitions are second order anyhow, or have only a small latent heat. And, I mean, high latent heat does not imply that you can extract large amounts of work from the cycle? <BR/><BR/>What I am more puzzled about is this question if Paul'sstefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-35079760298921032332007-12-04T17:38:00.000-05:002007-12-04T17:38:00.000-05:00Hi Thomas Larsson,Could you provide a web referenc...Hi Thomas Larsson,<BR/><BR/>Could you provide a web reference discussing the 3D Ising?<BR/><BR/>I would be interested in comparing this to the work of RD MacPherson and DJ Srolovitz.<BR/><BR/>I sincerely doubt that I "will be rich and famous", but I am curious.Doughttps://www.blogger.com/profile/07643919214761722345noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-89821906926498199522007-12-04T05:31:00.000-05:002007-12-04T05:31:00.000-05:00Doug,A lot is known about 3D Ising approximately -...Doug,<BR/><BR/>A lot is known about 3D Ising approximately - computer simulations, high temp expansions, low temp expansions, expansions in the number of dimensions (4-epsilon or 2+epsilon), etc. As for exact results in 3D: well, if you find some, you will be rich and famous.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-2914875194713977422007-12-03T23:54:00.000-05:002007-12-03T23:54:00.000-05:00Hi Stefan and Bee,1 - There may be a means [beyond...Hi Stefan and Bee,<BR/><BR/>1 - There may be a means [beyond my ability] to extend this to 3D.<BR/><BR/>Perhaps for Onsager 2D to 3D, someone may be able use to techniques that extended John von Neumann 2D to 3D [and more?] structures.<BR/><BR/>RD MacPherson, DJ Srolovitz, “The von Neumann relation generalized to coarsening of three-dimensional microstructures”. [p1053]<BR/>doi:10.1038/Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-86316217030855749412007-12-03T20:02:00.000-05:002007-12-03T20:02:00.000-05:00Thanks for another great post. If I recall correc...Thanks for another great post. If I recall correctly from stat mech., originally Ising created his model assuming only 1 dimension, whhc has an exact solution. Later L. Onsager extended the model to 2D for which there is also an exact solution (as your equation there implies). But as I recall, there is no exact solution to the 3D extension of the Ising model?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-84177739544487309652007-12-03T18:42:00.000-05:002007-12-03T18:42:00.000-05:00Dear Stefan,I think one can make a Paul-type gadge...Dear Stefan,<BR/><BR/>I think one can make a Paul-type gadget around many phase transitions.<BR/><BR/>E.g., a solid close to its melting point at one atmosphere that expands on melting. You let the solid melt, and it does work = (one atmosphere)*(volume difference of liquid and solid). You then cool down the liquid to freeze it and repeat the cycle.<BR/><BR/>The work per cycle is fixed; the Arunhttps://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-66741902922855172432007-12-03T15:08:00.000-05:002007-12-03T15:08:00.000-05:00Hi Paul,that's a nice gadget you are proposing, an...Hi Paul,<BR/><BR/><BR/>that's a nice gadget you are proposing, and an interesting question.<BR/><BR/>One thing is not quite clear to me: What do you want to do with the current induced in the coil? Charge a battery or something like that? The direction of the current will have opposite directions when magntisation emerges and vanishes within one cycle, and the direction of the current when stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-47379975449586583282007-12-03T11:46:00.000-05:002007-12-03T11:46:00.000-05:00Hi Stefan and Bee --Thanks for bringing up the sub...Hi Stefan and Bee --<BR/><BR/>Thanks for bringing up the subject of spontaneous magnetization at the Curie transition. It is certainly interesting physics, and also it gives me a chance to ask for your answer(s) to an old puzzler. <BR/><BR/>Suppose we propose the following idea for a goofy kind of heat engine. Take a piece of ferromagnetic material and surround it with an coil of wire Anonymousnoreply@blogger.com