scholarly journals Large N and bosonization in three dimensions

2012 ◽  
Vol 2012 (10) ◽  
Author(s):  
Aleksey Cherman ◽  
Daniele Dorigoni
Keyword(s):  
Three Dimensions ◽  
Large N

scholarly journals The cubic fixed point at large N

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Damon J. Binder
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
Ising Models ◽  
Three Dimensions ◽  
Renormalization Group Flow ◽  
Conformal Bootstrap ◽  
Large N ◽  
Group Flow ◽  
3D Ising Model

Abstract By considering the renormalization group flow between N coupled Ising models in the UV and the cubic fixed point in the IR, we study the large N behavior of the cubic fixed points in three dimensions. We derive a diagrammatic expansion for the 1/N corrections to correlation functions. Leading large N corrections to conformal dimensions at the cubic fixed point are then evaluated using numeric conformal bootstrap data for the 3d Ising model.

scholarly journals Sociocultural, economic and ethnic homogeneity in residential mobility and spatial sorting among couples

2019 ◽  
Vol 51 (4) ◽  
pp. 891-912 ◽  
Author(s):  
Wouter van Gent ◽  
Marjolijn Das ◽  
Sako Musterd
Keyword(s):  
Large Scale ◽  
Economic Status ◽  
Three Dimensions ◽  
Household Level ◽  
Large N ◽  
Spatial Sorting ◽  
Neighbourhood Level ◽  
Mobility Behaviour ◽  
Sociocultural Characteristics ◽  
Distribution Of Income

This study aims to advance the spatial conceptualization of ‘social homophily’ by relating the match, or mismatch, between a household’s social and sociocultural characteristics and the characteristics of the neighbourhood of residence to the probability of moving away from that neighbourhood. Three matching dimensions were investigated: economic status, ethnic background and sociocultural disposition. This paper’s focus is on the sociocultural dimension because this has not been included extensively in large-scale research so far. Initially we investigate how level of education at the household level interacts with education composition at the neighbourhood level. To further investigate the sociocultural dimension, we then include the share of each partner’s income in the total household income in our analyses. Based on the spatial literature at the intersections of class, gender and family, we assume that, together with higher education, the intra-household distribution of income reflects a broader set of sociocultural values. We make use of large- N register data to analyse the residential and mobility behaviour of all registered stable couples in the four largest Dutch urban regions between 2008 and 2009. Our analyses indicate that the degree to which a household ‘matches’ its social surroundings negatively affects its probability of leaving. This is the case for all three dimensions, with sociocultural disposition having the largest effect. The conclusion reflects on the importance of these findings for social homophily, sorting and residential segregation, and proposes directions for further research.

Conditions governing the generalisation of threshold bound states by N attractive delta potentials in one and three dimensions

Open Physics ◽  
2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Marappan Dharani ◽  
Basudeb Sahu ◽  
Chakrakodi Shastry
Keyword(s):  
Bound States ◽  
Good Description ◽  
Threshold Energy ◽  
Delta Function ◽  
Bound State ◽  
Three Dimensions ◽  
Algebraic Equations ◽  
Integer Coefficients ◽  
Large N ◽  
Energy Bound

AbstractThis paper proves that for N attractive delta function potentials the number of bound states (Nb) satisfies 1 ≤ N b ≤ N in one dimension (1D), and is 0 ≤ N b ≤ N in three dimensions (3D). Algebraic equations are obtained to evaluate the bound states generated by N attractive delta potentials. In particular, in the case of N attractive delta function potentials having same separation a between adjacent wells and having the same strength λV, the parameter g=λVa governs the number of bound states. For a given N in the range 1–7, both in 1D and 3D cases the numerical values of gn, where n=1,2,..N are obtained. When g=gn, Nb ≤ n where Nb includes one threshold energy bound state. Furthermore, gn are the roots of the Nth order polynomial equations with integer coefficients. Based on our numerical calculations up to N=40, even when N becomes large, 0 ≤ g n ≤ 4 and $\frac{{\Sigma g_n }} {N} \simeq 2 $ and this result is expected to be generally valid. Thus, for g > 4 there will be no threshold or zero energy bound state, and if g≈ 2 for a given large N, the number of bound states will be approximately N/2. The empirical formula gn = 4/[1+exp((N 0 − n)/β)] gives a good description of the variation of gn as a function of n. This formula is useful in estimating the number of bound states for any N and g both in 1D and 3D cases.

Random matrix theory and ribonucleic acid (RNA) folding

2018 ◽  
Author(s):  
Antonia Tulino ◽  
Sergio Verdu
Keyword(s):  
Random Matrix Theory ◽  
Physical Interpretation ◽  
Random Matrix ◽  
Mechanical Model ◽  
Rna Folding ◽  
Matrix Theory ◽  
Three Dimensions ◽  
Large N ◽  
Rna Pseudoknots ◽  
The Matrix

This article discusses a series of recent applications of random matrix theory (RMT) to the problem of RNA folding. It first provides a schematic overview of the RNA folding problem, focusing on the concept of RNA pseudoknots, before considering a simplified framework for describing the folding of an RNA molecule; this framework is given by the statistic mechanical model of a polymer chain of L nucleotides in three dimensions with interacting monomers. The article proceeds by presenting a physical interpretation of the RNA matrix model and analysing the large-N expansion of the matrix integral, along with the pseudoknotted homopolymer chain. It extends previous results about the asymptotic distribution of pseudoknots of a phantom homopolymer chain in the limit of large chain length.

THE CHERN–SIMONS TERM AND THE DYNAMICS OF THE CPn−1 MODEL IN THREE DIMENSIONS

1992 ◽  
Vol 07 (03) ◽  
pp. 619-630 ◽  
Author(s):  
E. ABDALLA ◽  
F. M. DE CARVALHO
Keyword(s):  
Phase Structure ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Three Dimensions ◽  
Rich Phase ◽  
Large N ◽  
Dimensional Space Time ◽  
Chern Simons ◽  
Three Dimensional Space

We analyze the phase structure of the CPn−1 model in three-dimensional space–time coupled to fermions, paying special attention to the role played by the Chern–Simons term generated by the fermions. A rich phase structure arises from the large-n expansion.

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