Revision as of 18:48, 10 June 2025 edit Stepwise Continuous Dysfunction (talk \| contribs) Extended confirmed users 1,114 edits →Two dimensions: move a lot of details that are excessive here over to Square lattice Ising model (since we're calling that the "main article" for this section, let's treat it that way) ← Previous edit		Revision as of 19:06, 10 June 2025 edit undo Stepwise Continuous Dysfunction (talk \| contribs) Extended confirmed users 1,114 edits →Historical significance: bringing Democritus into this has a rather "since Man first looked up at the stars in wonder" feel; it also makes overly strong claims about the views of a figure only known through fragments and indirect testimony Next edit →
Line 144: ==Historical significance== One of [[Democritus]]' arguments in support of [[atomism]] was that atoms naturally explain the sharp phase boundaries observed in materials{{citation needed\|date=July 2014}}, as when ice melts to water or water turns to steam. His idea was that small changes in atomic-scale properties would lead to big changes in the aggregate behavior. Others believed that matter is inherently continuous, not atomic, and that the large-scale properties of matter are not reducible to basic atomic properties. While the laws of chemical bonding made it clear to nineteenth century chemists that atoms were real, among physicists the debate continued well into the early twentieth century. Atomists, notably [[James Clerk Maxwell]] and [[Ludwig Boltzmann]], applied Hamilton's formulation of Newton's laws to large systems, and found that the [[statistical mechanics\|statistical behavior]] of the atoms correctly describes room temperature gases. But classical statistical mechanics did not account for all of the properties of liquids and solids, nor of gases at low temperature. Once modern [[quantum mechanics]] was formulated, atomism was no longer in conflict with experiment, but this did not lead to a universal acceptance of statistical mechanics, which went beyond atomism. [[Josiah Willard Gibbs]] had given a complete formalism to reproduce the laws of thermodynamics from the laws of mechanics. But many faulty arguments survived from the 19th century, when statistical mechanics was considered dubious. The lapses in intuition mostly stemmed from the fact that the limit of an infinite statistical system has many [[Zero–one law\|zero-one laws]] which are absent in finite systems: an infinitesimal change in a parameter can lead to big differences in the overall, aggregate behavior~~, as Democritus expected~~. ===No phase transitions in finite volume===

Ising model: Difference between revisions