Within the exact renormalisation group, the scaling solutions for O(N) symmetric scalar field theories are studied to leading order in the derivative expansion. The Gaussian fixed point is examined for d > 2 dimensions and arbitrary infrared regularisation. The Wilson-Fisher fixed point in d = 3 is studied using an optimised flow. We compute critical exponents and subleading corrections-to-scal...

We shall now use the results of the previous chapters to derive explicitly the critical exponents of the O(N)-symmetric φ 4-theory. The unique tensor multiplying the product of fields φ α φ β φ γ φ δ in the interaction is [recall (6.25)]

We report on a high statistics numerical study of the crystalline random surface model with extrinsic curvature on lattices of up to 64 points. The critical exponents at the crumpling transition are determined by a number of methods all of which are shown to agree within estimated errors. The correlation length exponent is found to be ν = 0.71(5) from the tangenttangent correlation function whe...

We study the behavior of scale-free networks, having connectivity distribution P(k) approximately k(-lambda), close to the percolation threshold. We show that for networks with 3<lambda<4, known to undergo a transition at a finite threshold of dilution, the critical exponents are different than the expected mean-field values of regular percolation in infinite dimensions. Networks with 2<lambda<...

The critical behaviour of Mn0.94Nb0.06CoGe alloy around the paramagnetic-ferromagnetic phase transition was studied based on the field dependence on magnetic entropy change. By using the obtained exponents, the modified Arrott plot is consistent with that by using conventional method. These critical exponents are confirmed by the Widom scaling relation. Based on these critical exponents, the ma...

We use a three-dimensional massive field theory up to the two-loop approximation to study the critical behavior of semi-infinite quenched random Ising-like systems at the special surface transition. Besides, we extend up to the next-to leading order, the previous first-order results of the sqrt[epsilon] expansion obtained by Ohno and Okabe [Phys. Rev. B 46, 5917 (1992)]. The numerical estimates...

We argue that the sharp-cuto Wilson renormalization group provides a powerful tool for the analysis of second-order and weakly rst-order phase transitions. In particular, in a computation no harder than the calculation of the 1-loop e ective potential, we show that the Wilson RG yields the xed point couplings and critical exponents of 3-dimensional O(N) scalar eld theory, with results close to ...

Over an alphabet of size 3 we construct an infinite balanced word with critical exponent 2 + √ 2/2. Over an alphabet of size 4 we construct an infinite balanced word with critical exponent (5 + √ 5)/4. Over larger alphabets, we give some candidates for balanced words (found computationally) having small critical exponents. We also explore a method for proving these results using the automated t...