Unbiased sampling of globular lattice proteins in three dimensions

We present a Monte Carlo method that allows efficient and unbiased sampling of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit each lattice site exactly once. They are often used as simple models of globular proteins, upon adding suitable local interactions. Our algorithm can easily be equipped with such interactions, but we study here mainly the flexible homopolymer case where each conformation is generated with uniform probability. We argue that the algorithm is ergodic and has dynamical exponent z=0. We then use it to study polymers of size up to 64^3 = 262144 monomers. Results are presented for the effective interaction between end points, and the interaction with the boundaries of the system

Marriage, Specialization, and the Gender Division of Labor

A customary gender division of labor is one in which women and men are directed towards certain tasks and/or explicitly prohibited from performing others. We offer an explanation as to why the gender division of labor is so often enforced by custom, and why customary gender divisions of labor generally involve both direction and prohibition. Our model builds on the literature on the marital hold-up problem, and considers both problems in choice of specialty and human capital acquisition in a framework in which agents learn a variety of skills and must search for a marriage partner on the marriage market. We show that wasteful behavior may emerge due to strategic incentives in career choice and human capital acquisition, and that both problems may be mitigated through the customary gender division of labor. We find, however, that a gender division of labor is not Pareto-improving; one gender is made worse off. Both the distributional effects and welfare gains to a customary gender division of labor decrease as opportunities to exchange in markets increase.

Marriage, Specialization, and the Gender Division of Labor

A customary gender division of labor is one in which women and men are directed towards certain tasks and/or explicitly prohibited from performing others. We offer an explanation as to why the gender division of labor is so often enforced by custom, and why customary gender divisions of labor generally involve both direction and prohibition. Our model builds on the literature on the marital hold-up problem, and considers both problems in choice of specialty and human capital acquisition in a framework in which agents learn a variety of skills and then enter the marriage market. We show that wasteful behavior may emerge due to strategic incentives in career choice and human capital acquisition, and that both problems may be mitigated through the customary gender division of labor. We find, however, that a gender division of labor is not Pareto-improving; one gender is made worse off. Both the distributional effects and welfare gains of a customary gender division of labor decrease as opportunities to exchange in markets increase.earnings inequality, income inequality, gender, race, and ethnicity differences

A Human Capital-Based Theory of Post Marital Residence Rules

In pre-modern societies the residence of a newly-wedded couple is often decided by custom. We formulate a theory of optimal post-marital residence rules based on contracting problems created by the nature of pre-marriage human capital investments. We argue that a fixed post-marital residence rule may mitigate a hold-up problem by specifying marriage terms and limiting possibilities for renegotiation; the trade-off is that the rule may prohibit beneficial renegotiation of post-marital location. A point of interest of our approach is that the magnitude and direction of transfers accompanying marriage are endogenous. We apply our theoretical results to understanding cross-cultural post-marital residence patters. We find some predictive ability in variables related to outside options, control over the environment, and potential degree of social control.Marriage, Bargaining, Hold-up Problem, Dowry, Bride-Price

A Human Capital-Based Theory of Post-Marital Residence Rules

In pre-modern societies the residence of a newly-wedded couple is often decided by custom. While researchers have analyzed factors leading to particular post-marital residence patterns, no one has explained why a society should have a customary rule in the first place. Our theory stems from contracting problems created by the nature of pre-marriage human capital investments. We argue that a fixed post-marital residence rule may solve a hold-up problem by specifying marriage terms and limiting possibilities for renegotiation; the trade-off is the rule may prohibit beneficial renegotiation of post-marital location. We compare alternative residence rules (or lack thereof) under different degrees of location specificity of human capital and environmental uncertainty. We apply our theoretical results to Murdock's (1967) 862-society data set, augmented with climate data. We find some predictive ability in variables related to outside options, control over the environment, and potential degree of social control.

Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the Potts model

By relating the ground state of Temperley-Lieb hamiltonians to partition functions of 2D statistical mechanics systems on a half plane, and using a boundary Coulomb gas formalism, we obtain in closed form the valence bond entanglement entropy as well as the valence bond probability distribution in these ground states. We find in particular that for the XXX spin chain, the number N_c of valence bonds connecting a subsystem of size L to the outside goes, in the thermodynamic limit, as = (4/pi^2) ln L, disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/(3 ln 2) ln L. Our results generalize to the Q-state Potts model.Comment: 4 pages, 2 figure

Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model

The two-dimensional Potts model can be studied either in terms of the original Q-component spins, or in the geometrical reformulation via Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for arbitrary real values of Q by construction, it was only shown very recently that the spin representation can be promoted to the same level of generality. In this paper we show how to define the Potts model in terms of observables that simultaneously keep track of the spin and FK degrees of freedom. This is first done algebraically in terms of a transfer matrix that couples three different representations of a partition algebra. Using this, one can study correlation functions involving any given number of propagating spin clusters with prescribed colours, each of which contains any given number of distinct FK clusters. For 0 <= Q <= 4 the corresponding critical exponents are all of the Kac form h_{r,s}, with integer indices r,s that we determine exactly both in the bulk and in the boundary versions of the problem. In particular, we find that the set of points where an FK cluster touches the hull of its surrounding spin cluster has fractal dimension d_{2,1} = 2 - 2 h_{2,1}. If one constrains this set to points where the neighbouring spin cluster extends to infinity, we show that the dimension becomes d_{1,3} = 2 - 2 h_{1,3}. Our results are supported by extensive transfer matrix and Monte Carlo computations.Comment: 15 pages, 3 figures, 2 table

Extended two-level quantum dissipative system from bosonization of the elliptic spin-1/2 Kondo model

We study the elliptic spin-1/2 Kondo model (spin-1/2 fermions in one dimension with fully anisotropic contact interactions with a magnetic impurity) in the light of mappings to bosonic systems using the fermion-boson correspondence and associated unitary transformations. We show that for fixed fermion number, the bosonic system describes a two-level quantum dissipative system with two noninteracting copies of infinitely-degenerate upper and lower levels. In addition to the standard tunnelling transitions, and the transitions driven by the dissipative coupling, there are also bath-mediated transitions between the upper and lower states which simultaneously effect shifts in the horizontal degeneracy label. We speculate that these systems could provide new examples of continuous time quantum random walks, which are exactly solvable.Comment: 7 pages, 1 figur

Selfduality for coupled Potts models on the triangular lattice

We present selfdual manifolds for coupled Potts models on the triangular lattice. We exploit two different techniques: duality followed by decimation, and mapping to a related loop model. The latter technique is found to be superior, and it allows to include three-spin couplings. Starting from three coupled models, such couplings are necessary for generating selfdual solutions. A numerical study of the case of two coupled models leads to the identification of novel critical points