## Duality and form factors in the thermally deformed two-dimensional tricritical Ising model

Axel Cortés Cubero, Robert M. Konik, Máté Lencsés, Giuseppe Mussardo, Gabor Takács

SciPost Phys. 12, 162 (2022) · published 16 May 2022

- doi: 10.21468/SciPostPhys.12.5.162
- Submissions/Reports

### Abstract

The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional $E_7$ Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation operators, $\sigma(x)$ and $\sigma'(x)$, in either phase are accompanied by associated disorder operators, $\mu(x)$ and $\mu'(x)$. Working specifically in the high temperature phase, we write down the sets of bootstrap equations for these four operators. For $\sigma(x)$ and $\sigma'(x)$, the equations are identical in form and are parameterised by the values of the one-particle form factors of the two lightest $\mathbb{Z}_2$ odd particles. Similarly, the equations for $\mu(x)$ and $\mu'(x)$ have identical form and are parameterised by two elementary form factors. Using the clustering property, we show that these four sets of solutions are eventually not independent; instead, the parameters of the solutions for $\sigma(x)/\sigma'(x)$ are fixed in terms of those for $\mu(x)/\mu'(x)$. We use the truncated conformal space approach to confirm numerically the derived expressions of the matrix elements as well as the validity of the $\Delta$-sum rule as applied to the off-critical correlators. We employ the derived form factors of the order and disorder operators to compute the exact dynamical structure factors of the theory, a set of quantities with a rich spectroscopy which may be directly tested in future inelastic neutron or Raman scattering experiments.

### Cited by 5

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Axel Cortes Cubero, -
^{2}Robert Konik, -
^{3}Máté Lencsés, -
^{4}^{5}Giuseppe Mussardo, -
^{3}Gábor Takács

^{1}University of Puerto Rico-Mayaguez [UPRM]^{2}Brookhaven National Laboratory [BNL]^{3}Budapesti Műszaki és Gazdaságtudományi Egyetem / Budapest University of Technology and Economics [BUTE]^{4}Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies [SISSA]^{5}Istituto Nazionale di Fisica Nucleare (presso la SISSA) / National Institute of Nuclear Physics (at SISSA) [INFN at SISSA]

- Consiglio Nazionale delle Ricerche (CNR) (through Organization: Consiglio Nazionale Delle Ricerche / Italian National Research Council [CNR])
- Magyar Tudományos Akadémia / Hungarian Academy of Sciences [MTA]
- Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) (through Organization: Ministero dell'Istruzione, dell'Università e della Ricerca / Ministry of Education, Universities and Research [MIUR])
- Nemzeti Kutatási, Fejlesztési és Innovációs Hivatal / National Research, Development and Innovation Office [NKFIH]
- United States Department of Energy [DOE]