The evolution of industrial policy in the United Kingdom, 1964-1978

The thesis focuses on policy measures between 196A and 1978 to improve performance and growth in U.K.'s private industry. Underlying structural weaknesses and institutional constraints characteristic to U.K.'s company sector are identified and analysed in Part One. This exercise provides the basis for both a definition of the concept of "industrial policy" and a critical assessment in Part Two of its relevance and effectiveness to tackle industry's main difficulties. In discussing policy initiatives to assist companies with public funds for investment finance, industrial reorganisation and the application of new technology, a variety of problems associated with state intervention in private industry are highlighted. The various attempts by policy-makers to overcome shortcomings in the coordination of policy, communication with firms, public monitoring and exercise of control as a result of experience with existing measures and by means of new, more powerful instruments are examined in detail. Industry's growing difficulties and pressure on policy-makers to expand or at least improve public assistance meant that industry policy evolved, despite controversy and policy shifts, with a certain degree of continuity. In the three case-studies which follow, shipbuilding, computers and the NEB, these dynamics are explored in depth. One useful contribution of this thesis is to explain industrial decline in the U.K. economy in terms of supply-side constraints in the private sector. This approach avoids the methodological shortcomings of currently popular theories which instead concentrate on factors outside private industry, such as the public sector or international trade. The analysis of overall industrial policy since 1$6A and the attempt to develop criteria for assessing its effectiveness contribute to a better understanding of this subject. The case studies cover new areas of research. By linking the analysis of policy-making with theoretical hypotheses concerning industry's main problems the effects of policy measures in private industry can be evaluated to determine both the limitations and the potential of state intervention in private industry

Critical behaviour of the two-dimensional Ising susceptibility

We report computations of the short-distance and the long-distance (scaling) contributions to the square-lattice Ising susceptibility in zero field close to T_c. Both computations rely on the use of nonlinear partial difference equations for the correlation functions. By summing the correlation functions, we give an algorithm of complexity O(N^6) for the determination of the first N series coefficients. Consequently, we have generated and analysed series of length several hundred terms, generated in about 100 hours on an obsolete workstation. In terms of a temperature variable, \tau, linear in T/T_c-1, the short-distance terms are shown to have the form \tau^p(ln|\tau|)^q with p>=q^2. To O(\tau^14) the long-distance part divided by the leading \tau^{-7/4} singularity contains only integer powers of \tau. The presence of irrelevant variables in the scaling function is clearly evident, with contributions of distinct character at leading orders |\tau|^{9/4} and |\tau|^{17/4} being identified.Comment: 11 pages, REVTex

Partially directed paths in a wedge

The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetric wedge defined by $Y = \pm pX$, and an asymmetric wedge defined by the lines $Y= pX$ and Y=0, where $p > 0$ is an integer. We prove that the growth constant for all these models is equal to $1+\sqrt{2}$, independent of the angle of the wedge. We derive functional recursions for both models, and obtain explicit expressions for the generating functions when $p=1$. From these we find asymptotic formulas for the number of partially directed paths of length $n$ in a wedge when $p=1$. The functional recurrences are solved by a variation of the kernel method, which we call the ``iterated kernel method''. This method appears to be similar to the obstinate kernel method used by Bousquet-Melou. This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to find simple explicit expressions for them. However, in spite of this, the generating functions turn out to be similar in form to Jacobi $\theta$-functions, and have natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT

Critical parameters of N-vector spin models on 3d lattices from high temperature series extended to order beta^{21}

High temperature expansions for the free energy, the susceptibility and the second correlation moment of the classical N-vector model [also denoted as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] have been extended to order beta^{21} on the simple cubic and the body centered cubic lattices, for arbitrary N. The series for the second field derivative of the susceptibility has been extended to order beta^{17}. An analysis of the newly computed series yields updated estimates of the model's critical parameters in good agreement with present renormalization group estimates.Comment: 3 pages, Latex,(fleqn.sty, espcrc2.sty) no figures, contribution to Lattice'97 to appear in Nucl. Phys. Proc. Supp

New Algorithm of the Finite Lattice Method for the High-temperature Expansion of the Ising Model in Three Dimensions

We propose a new algorithm of the finite lattice method to generate the high-temperature series for the Ising model in three dimensions. It enables us to extend the series for the free energy of the simple cubic lattice from the previous series of 26th order to 46th order in the inverse temperature. The obtained series give the estimate of the critical exponent for the specific heat in high precision.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Letter

Force induced triple point for interacting polymers

We show the existence of a force induced triple point in an interacting polymer problem that allows two zero-force thermal phase transitions. The phase diagrams for three different models of mutually attracting but self avoiding polymers are presented. One of these models has an intermediate phase and it shows a triple point but not the others. A general phase diagram with multicritical points in an extended parameter space is also discussed.Comment: 4 pages, 8 figures, revtex

Low temperature series expansions for the square lattice Ising model with spin S > 1

We derive low-temperature series (in the variable $u = \exp[-\beta J/S^2]$) for the spontaneous magnetisation, susceptibility and specific heat of the spin-$S$ Ising model on the square lattice for $S=\frac32$, 2, $\frac52$, and 3. We determine the location of the physical critical point and non-physical singularities. The number of non-physical singularities closer to the origin than the physical critical point grows quite rapidly with $S$. The critical exponents at the singularities which are closest to the origin and for which we have reasonably accurate estimates are independent of $S$. Due to the many non-physical singularities, the estimates for the physical critical point and exponents are poor for higher values of $S$, though consistent with universality.Comment: 14 pages, LaTeX with IOP style files (ioplppt.sty), epic.sty and eepic.sty. To appear in J. Phys.