@article {660, title = {Critical points in coupled Potts models and correlated percolation}, journal = {J. Stat. Mech. Theor. Exp.}, volume = {2023}, year = {2023}, pages = {013203}, abstract = {We use scale invariant scattering theory to exactly determine the renormalization group fixed points of a q-state Potts model coupled to an r-state Potts model in two dimensions. For integer values of q and r the fixed point equations are very constraining and show in particular that scale invariance in coupled Potts ferromagnets is limited to the Ashkin-Teller case (q = r = 2). Since our results extend to continuous values of the number of states, we can access the limit r {\textrightarrow} 1 corresponding to correlated percolation, and show that the critical properties of Potts spin clusters cannot in general be obtained from those of Fortuin-Kasteleyn clusters by analytical continuation.}, doi = {10.1088/1742-5468/aca901}, url = {https://iopscience.iop.org/article/10.1088/1742-5468/aca901}, author = {Noel Lamsen and Youness Diouane and Gesualdo Delfino} } @article {661, title = {On the RPᴺ$^{-}${\textonesuperior} and CPᴺ$^{-}${\textonesuperior} universality classes}, journal = {J. Stat. Mech. Theor. Exp.}, volume = {2023}, year = {2023}, pages = {043204}, abstract = {We recently determined the exact fixed point equations and the spaces of solutions of the two-dimensional RPᴺ$^{-}${\textonesuperior} and CPᴺ$^{-}${\textonesuperior} models using scale invariant scattering theory. Here, we discuss subtleties hidden in some solutions and related to the difference between ferromagnetic and antiferromagnetic interaction.}, doi = {10.1088/1742-5468/acc8c9}, url = {https://iopscience.iop.org/article/10.1088/1742-5468/acc8c9}, author = {Youness Diouane and Noel Lamsen and Gesualdo Delfino} } @article {659, title = {Critical points in the CPᴺ$^{-}${\textonesuperior} model}, journal = {J. Stat. Mech. Theor. Exp.}, volume = {2022}, year = {2022}, pages = {023201}, abstract = {We use scale invariant scattering theory to obtain the exact equations determining the renormalization group fixed points of the two-dimensional CPᴺ$^{-}${\textonesuperior} model, for N real. Also due to special degeneracies at N = 2 and 3, the space of solutions for N >= 2 reduces to that of the O(N{\texttwosuperior} - 1) model, and accounts for a zero temperature critical point. For N < 2 the space of solutions becomes larger than that of the O(N{\texttwosuperior} - 1) model, with the appearance of new branches of fixed points relevant for criticality in gases of intersecting loops.}, doi = {10.1088/1742-5468/ac4983}, url = {https://iopscience.iop.org/article/10.1088/1742-5468/ac4983}, author = {Youness Diouane and Noel Lamsen and Gesualdo Delfino} } @article {658, title = {Critical points in the RPᴺ$^{-}${\textonesuperior} model}, journal = {J. Stat. Mech. Theor. Exp.}, volume = {2021}, year = {2021}, pages = {033214}, abstract = {The space of solutions of the exact renormalization group fixed point equations of the two-dimensional RPᴺ$^{-}${\textonesuperior} model, which we recently obtained within the scale invariant scattering framework, is explored for continuous values of N >= 0. Quasi-long-range order occurs only for N = 2, and allows for several lines of fixed points meeting at the Berezinskii-Kosterlitz-Thouless transition point. A rich pattern of fixed points is present below N* = 2.244 21. . , while only zero temperature criticality in the O(N(N + 1)/2 - 1) universality class can occur above this value. The interpretation of an extra solution at N = 3 requires the identification of a path to criticality specific to this value of N.}, doi = {10.1088/1742-5468/abe6fc}, url = {https://iopscience.iop.org/article/10.1088/1742-5468/abe6fc}, author = {Youness Diouane and Noel Lamsen and Gesualdo Delfino} } @article {657, title = {Absence of nematic quasi-long-range order in two-dimensional liquid crystals with three director components}, journal = {J. Phys. A Math. Theor.}, volume = {54}, year = {2020}, pages = {03LT01}, abstract = {The Lebwohl-Lasher model describes the isotropic-nematic transition in liquid crystals. In two dimensions, where its continuous symmetry cannot break spontaneously, it is investigated numerically since decades to verify, in particular, the conjecture of a topological transition leading to a nematic phase with quasi-long-range order. We use scale invariant scattering theory to exactly determine the renormalization group fixed points in the general case of N director components (RPᴺ$^{-}${\textonesuperior} model), which yields the Lebwohl-Lasher model for N = 3. For N > 2 we show the absence of quasi-long-range order and the presence of a zero temperature critical point in the universality class of the O(N(N + 1)/2 - 1) model. For N = 2 the fixed point equations yield the Berezinskii-Kosterlitz-Thouless transition required by the correspondence RP{\textonesuperior} \~{} O(2).}, doi = {10.1088/1751-8121/abd2fc}, url = {https://iopscience.iop.org/article/10.1088/1751-8121/abd2fc}, author = {Gesualdo Delfino and Youness Diouane and Noel Lamsen} }