Critical behavior of the second harmonic in a density wave system

Crystalline-like ordering of 8CB liquid crystals revealed by time-domain Brillouin scattering

We demonstrate that time-domain Brillouin scattering (TDBS), a technique based on an ultrafast pump-probe approach, is sensitive to phase transitions and apply it to the study of structural changes in 8CB liquid crystals at different temperatures across the isotropic, nematic, smectic, and crystalline phases. We investigate the viscoelastic properties of 8CB squeezed in a narrow gap, from the nanometer to submicrometer thickness range, and conclude on the long-range molecular structuring of the smectic phase. These TDBS results reveal that confinement effects favor structuring of the smectic phase into a crystallinelike phase that can be observed at wide distances far beyond the molecular dimensions.

Fractal dimension of critical curves in the O(n)-symmetric ϕ^{4} model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY, and Heisenberg models

We calculate the fractal dimension d_{f} of critical curves in the O(n)-symmetric (ϕ[over ⃗]^{2})^{2} theory in d=4-ε dimensions at 6-loop order. This gives the fractal dimension of loop-erased random walks at n=-2, self-avoiding walks (n=0), Ising lines (n=1), and XY lines (n=2), in agreement with numerical simulations. It can be compared to the fractal dimension d_{f}^{tot} of all lines, i.e., backbone plus the surrounding loops, identical to d_{f}^{tot}=1/ν. The combination ϕ_{c}=d_{f}/d_{f}^{tot}=νd_{f} is the crossover exponent, describing a system with mass anisotropy. Introducing a self-consistent resummation procedure and combining it with analytic results in d=2 allows us to give improved estimates in d=3 for all relevant exponents at 6-loop order.

Critical structure factors of bilinear fields in O(N) vector models

We compute the two-point correlation functions of general quadratic operators in the high-temperature phase of the three-dimensional O(N) vector model by using field-theoretical methods. In particular, we study the small- and large-momentum behavior of the corresponding scaling functions, and give general interpolation formulas based on a dispersive approach. Moreover, we determine the crossover exponent phi(T) associated with the traceless tensorial quadratic field, by computing and analyzing its six-loop perturbative expansion in fixed dimension. We find phi(T)=1.184(12), phi(T)=1.271(21), and phi(T)=1.40(4) for N=2,3,5, respectively.