COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |
University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Lecture 5 - The interacting dimer model
Lecture 5 - The interacting dimer modelAdd to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact INI IT. This talk has been canceled/deleted The aim of this minicourse is to present recent results, obtained together with Vieri Mastropietro (arXiv:1406.7710 and arXiv:1612.01274), on non-integrable perturbations of the classical dimer model on the square lattice. In the integrable situation, the model is free-fermionic and the large-scale fluctuations of its height function tend to a two-dimensional massless Gaussian field (GFF). We prove that convergence to GFF holds also for sufficiently small non-integrable perturbations. At the same time, we show that the dimer-dimer correlations exhibit non-trivial critical exponents, continuously depending upon the strength of the interaction: the model belongs, in a suitable sense, to the `Luttinger liquid' universality class. The proofs are based on constructive Renormalization Group for interacting fermions in two dimensions. Contents: 1. Basics: the model, height function, interacting dimer model. The main results for the interacting model: GFF fluctuations and Haldane relation. 2. The non-interacting dimer model: Kasteleyn theory, thermodynamiclimit, long-distance asymptotics of correlations, GFF fluctuations. Fermionic representation of the non-interacting and of the interacting dimer model. 3. Multi-scale analysis of the free propagator, Feynman diagrams and dimensional estimates. Determinant expansion. Non-renormalized multiscale expansion. 4. Renormalized multiscale expansion. Running coupling constants. Beta function. 5. The reference continuum model (the `infrared fixed point'): the Luttinger model. Exact solvability of the Luttinger model. Bosonization. 6. Ward identities and anomalies. Schwinger-Dyson equation. Closed equation for the correlation functions. Comparison of the lattice model with the reference one. This talk is part of the Isaac Newton Institute Seminar Series series. This talk is included in these lists:This talk is not included in any other list Note that ex-directory lists are not shown. |
Other listsType the title of a new list here Genetics Seminar Climate week SeminarOther talksFractionating the human frontoparietal cortex: Combining meta-analytic and real-time optimization approaches Welcome and Introduction. Update from Centre for Mathematical Imaging in Healthcare Discovering the gene networks that regulate hunger PRESTIGE LECTURE - QUANTUM TECHNOLOGIES US National Longitudinal Lesbian Family Study: from Regan to Trump |