tag:blogger.com,1999:blog-5439168179960787195.post3819699173440678733..comments2024-03-28T17:13:01.117+10:00Comments on Condensed concepts: What can students learn from an Ising model simulation?Ross H. McKenziehttp://www.blogger.com/profile/09950455939572097456noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-5439168179960787195.post-90343835213006309172018-09-12T17:58:29.490+10:002018-09-12T17:58:29.490+10:00Btw, the history is cool: Ising solved the 1D case...Btw, the history is cool: Ising solved the 1D case in his Phd, left academia, physicists ignored the 2D model but engineers used it, the Peirls got an approximate solutions and then the rest of physicists had their attention on it...jinaweehttps://www.blogger.com/profile/11404631188349293684noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-18664607902079174702018-09-12T17:54:55.665+10:002018-09-12T17:54:55.665+10:00On the theory part: I really enjoyed all the possi...On the theory part: I really enjoyed all the possible ways of solving the problem, from Onsager's to Feynman's method. The dependence on dimensions. All the approximate solutions. The link with QFT and RG, although I think it's not a complete analogy since it's a first order transition. The correspondence with the bosonic string...<br /><br />Regarding the simulation, I liked things which are more related to computer science, like noticing it's a Markov chain.jinaweehttps://www.blogger.com/profile/11404631188349293684noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-15498825844729250232018-09-11T22:32:48.530+10:002018-09-11T22:32:48.530+10:00The Ising model can also be useful to nucleation p...The Ising model can also be useful to nucleation processes (there is a nice JCP from Binder: https://aip.scitation.org/doi/pdf/10.1063/1.4959235). <br />You could also consider variants of the Ising model where specific spins are fixed either up or down to create walls that can help students to understand heterogeneous nucleation.RCRnoreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-31893867713137432592018-09-10T23:07:47.762+10:002018-09-10T23:07:47.762+10:00My own version, which I use in teaching fourth-yea...My own version, which I use in teaching fourth-year undergraduate and first-year graduate classes:<br /><a href="https://www.nottingham.ac.uk/~ppzscp/MC/" rel="nofollow">https://www.nottingham.ac.uk/~ppzscp/MC/</a><br /><br />I try to emphasise that the magnetisation is discontinuous across the first-order transition line (going from positive to negative h for T<Tc). You can "prove" this in the low-T limit, but I think it's still quite surprising.SPhttps://www.blogger.com/profile/05367562120686067753noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-37406086559826001142018-09-10T21:40:26.464+10:002018-09-10T21:40:26.464+10:00I'm not sure it's the appropriate place to...I'm not sure it's the appropriate place to introduce these topics but: Scale invariance and RG flow. See https://www.youtube.com/watch?v=MxRddFrEnPcAnonymousnoreply@blogger.com