2019/04/30 by Andreas Stergiou · 1 citation
Mathematics · Physics and Astronomy · #Antiferromagnetism #Black Holes and Theoretical Physics #Conformal map #Conformal symmetry #Field (mathematics) #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons #Phase (matter) #Phase transition #Symmetry (geometry) #Tetragonal crystal system #cond-mat.stat-mech #cond-mat.str-el #hep-th
paper · pdf · doi:10.21468/scipostphys.7.1.010
published as SciPost Phys. 7, 010 (2019) · 20 pages, 7 figures. v2: Some experimental and $\varepsilon$-expansion results added in the introduction. v3: Corrections regarding the applicability of our results to stacked triangular antiferromagnets. v4: Clarifications added. Applicability of our results to XY stacked triangular antiferromagnets reevaluated. v5: Further clarifying remarks added in Section 3
openalex publication_date 2019/07/17 · openalex created_date 2019/07/30 · arxiv created 2020/11/20 · arxiv updated 2020/11/23 · openalex updated_date 2026/08/05
Conformal field theories (CFTs) with MN and tetragonal global symmetry in d=2+1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions. As a result, they have been studied in great detail with the ε=4-d <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>ε</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> <mml:mo>−</mml:mo> <mml:mi>d</mml:mi> </mml:mrow> </mml:math> expansion and other field theory methods. The study of these theories with the nonperturbative numerical conformal bootstrap is initiated in this work. Bounds for operator dimensions are obtained and they are found to possess sharp kinks in the MN case, suggesting the existence of full-fledged CFTs. Based on the existence of a certain large- N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>N</mml:mi> </mml:math> expansion in theories with MN symmetry, these are argued to be the CFTs predicted by the ε <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>ε</mml:mi> </mml:math> expansion. In the tetragonal case no new kinks are found, consistently with the absence of such CFTs in the ε <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>ε</mml:mi> </mml:math> expansion. Estimates for critical exponents are provided for a few cases describing phase transitions in actual physical systems. In two particular MN cases, corresponding to theories with global symmetry groups O(2)2\rtimes S2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mn>2</mml:mn> <mml:msup> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>⋊</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> and O(2)3\rtimes S3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mn>2</mml:mn> <mml:msup> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>⋊</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> , a second kink is found. In the O(2)2\rtimes S2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mn>2</mml:mn> <mml:msup> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>⋊</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> case it is argued to be saturated by a CFT that belongs to a new universality class relevant for the structural phase transition of NbO 2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> and paramagnetic-helimagnetic transitions of the rare-earth metals Ho and Dy. In the O(2)3\rtimes S3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mn>2</mml:mn> <mml:msup> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>⋊</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> case it is suggested that the CFT that saturates the second kink belongs to a new universality class relevant for the paramagnetic-antiferromagnetic phase transition of the rare-earth metal Nd.