2017/11/30 by P. V. Sriluckshmy, P V Sriluckshmy, Ipsita Mandal
Physics and Astronomy · #Antiferromagnetism #Ferromagnetism #Ising model #Mutual information #Phase transition #Quantum many-body systems #Scaling #Spin glass #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/aab1b6
published as J. Stat. Mech. (2018) 043301 · minor updates; journal version accepted in JSTAT
openalex created_date 2017/11/17 · arxiv created 2018/03/13 · openalex publication_date 2018/04/01 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/06
Abstract Rényi mutual information, computed from second Rényi entropies, can identify classical phase transitions from their finite-size scaling at critical points. We apply this technique to examine the presence or absence of finite temperature phase transitions in various two-dimensional models on a square lattice, which are extensions of the conventional Ising model by adding a quenched disorder. When the quenched disorder causes the nearest neighbor bonds to be both ferromagnetic and antiferromagnetic, (a) a spin glass phase exists only at zero temperature, and (b) a ferromagnetic phase exists at a finite temperature when the antiferromagnetic bond distributions are sufficiently dilute. Furthermore, finite temperature paramagnetic-ferromagnetic transitions can also occur when the disordered bonds involve only ferromagnetic couplings of random strengths. In our numerical simulations, the ‘zero temperature only’ phase transitions are identified when there is no consistent finite-size scaling of the Rényi mutual information curves, while for finite temperature critical points, the curves can identify the critical temperature T c by their crossings at T c and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mn>2</mml:mn> <mml:mspace width="thinmathspace"/> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> </mml:msub> </mml:mstyle> </mml:math> .