{"paper":{"title":"Longitudinal fluctuations in the Berezinskii-Kosterlitz-Thouless phase","arxiv_id":"1606.04547","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-14T20:03:10+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v2","sentences":[{"i":0,"p":0.91,"id":"s0","own":true,"role":"contribution","text":"We analyze the interplay of longitudinal and transverse fluctuations in a $U(1)$ symmetric two-dimensional $\\phi^4$-theory.","hedge":{"p":0.77,"label":"asserted"},"own_p":0.9,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.16,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.09,"limitation":0.0,"future_work":0.0,"contribution":0.91,"interpretation":0.0}},{"i":1,"p":0.97,"id":"s1","own":true,"role":"method","text":"To this end, we derive coupled renormalization group equations for both types of fluctuations obtained from a linear (cartesian) decomposition of the order parameter field.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.96,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.97,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.0}},{"i":2,"p":0.88,"id":"s2","own":false,"role":"result","text":"Discarding the longitudinal fluctuations, the expected Berezinskii-Kosterlitz-Thouless (BKT) phase characterized by a finite stiffness and an algebraic decay of order parameter correlations is recovered.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.46,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.2,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.88,"background":0.1,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.02}},{"i":3,"p":0.98,"id":"s3","own":true,"role":"result","text":"Renormalized by transverse fluctuations, the longitudinal mass scales to zero, so that longitudinal fluctuations become increasingly important for small momenta.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.85,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.38,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.02}},{"i":4,"p":0.98,"id":"s4","own":true,"role":"result","text":"Within our expansion of the effective action, they generate a logarithmic decrease of the stiffness, in agreement with previous functional renormalization group calculations.","hedge":{"p":0.94,"label":"asserted"},"own_p":0.77,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.29,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.02}},{"i":5,"p":0.81,"id":"s5","own":true,"role":"interpretation","text":"The logarithmic terms imply a deviation from the vanishing beta-function for the stiffness in the non-linear sigma model describing the phase fluctuations at three-loop order.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.74,"main_claim_p":0.12,"quantitative":true,"quantitative_p":0.53,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.19,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.81}},{"i":6,"p":0.81,"id":"s6","own":true,"role":"method","text":"To gain further insight, we also compute the flow of the parameters characterizing longitudinal and transverse fluctuations from a density-phase representation of the order parameter field, with a cutoff on phase fluctuations.","hedge":{"p":0.87,"label":"asserted"},"own_p":0.95,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.18,"role_probabilities":{"gap":0.0,"method":0.81,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.19,"interpretation":0.0}},{"i":7,"p":0.98,"id":"s7","own":true,"role":"result","text":"The power-law flow of the longitudinal mass and other quantities is thereby confirmed, but the stiffness remains finite in this approach.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.27,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":8,"p":0.96,"id":"s8","own":true,"role":"interpretation","text":"We conclude that the marginal flow of the stiffness obtained in the cartesian representation is an artifact of the truncated expansion of momentum dependences.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.86,"main_claim_p":0.89,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.03,"background":0.0,"limitation":0.01,"future_work":0.0,"contribution":0.0,"interpretation":0.96}}]},"compiled":{"main_claim":{"p":1.0,"text":"We conclude that the marginal flow of the stiffness obtained in the cartesian representation is an 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