A Caltech Library Service

The random-bond Ising model in 2.01 and 3 dimensions

Komargodski, Zohar and Simmons-Duffin, David (2017) The random-bond Ising model in 2.01 and 3 dimensions. Journal of Physics A: Mathematical and Theoretical, 50 (15). Art. No. 154001. ISSN 1751-8113.

[img] PDF - Published Version
See Usage Policy.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2 < d < 4 this disorder is a relevant perturbation that drives the system to a new fixed point of the renormalization group. At d = 2 such disorder is marginally irrelevant and can be studied using conformal perturbation theory. Combining conformal perturbation theory with recent results from the conformal bootstrap we compute some scaling exponents in an expansion around d = 2. If one trusts these computations also in d = 3, one finds results consistent with experimental data and Monte Carlo simulations. In addition, we perform a direct uncontrolled computation in d = 3 using new results for low-lying operator dimensions and OPE coefficients in the 3d Ising model. We compare these new methods with previous studies. Finally, we comment about the O(2) model in d = 3, where we predict a large logarithmic correction to the infrared scaling of disorder.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Komargodski, Zohar0000-0002-8486-0811
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2017 IOP Publishing Ltd. Received 2 September 2016 Accepted 15 February 2017 Accepted Manuscript online 15 February 2017 Published 14 March 2017 We thank Amnon Aharony, Ofer Aharony, Leon Balents, Sean Hartnoll, Luca Iliesiu, Mehran Kardar, Igor Klebanov, Elias Kiritsis, Leonid Levitov, Andreas Ludwig, David Poland, Silviu Pufu, Leonardo Rastelli, Slava Rychkov, Tadashi Takayanagi, and Shimon Yankielowicz for useful discussions. We are especially grateful to John Cardy for essential comments and collaboration in the early stages of this work. DSD is supported by DOE grant number DE-SC0009988 and a William D. Loughlin Membership at the Institute for Advanced Study. ZK is supported in part by an Israel Science Foundation center for excellence grant and by the I-CORE program of the Planning and Budgeting Committee and the Israel Science Foundation (grant number 1937/12). ZK is also supported by the ERC STG grant 335182 and by the United States-Israel Bi-national Science Foundation (BSF) under grant 2010/629.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0009988
Institute for Advanced Study William D. Loughlin MembershipUNSPECIFIED
Israel Science FoundationUNSPECIFIED
Israeli Centers of Research Excellence1937/12
European Research Council (ERC)335182
United States-Israel Binational Science Foundation (BSF)2010/629
Subject Keywords:quantum field theory, conformal perturbation theory, disordered models
Issue or Number:15
Record Number:CaltechAUTHORS:20170817-110229744
Persistent URL:
Official Citation:Zohar Komargodski and David Simmons-Duffin 2017 J. Phys. A: Math. Theor. 50 154001
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80556
Deposited By: Ruth Sustaita
Deposited On:17 Aug 2017 19:45
Last Modified:03 Oct 2019 18:32

Repository Staff Only: item control page