An algorithmic proof for the completeness of two-dimensional Ising model

We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all its spin-spin coupling equal to i\pi/4 and all the parameters of the original model are contained in the local magnetic fields of the Ising model. This result has already been derived by using techniques from quantum information theory and by exploiting the universality of cluster states. Here we do not use the quantum formalism and hence make the completeness result accessible to a wide audience. Furthermore our method has the advantage of being algorithmic in nature so that by following a set of simple graphical transformations, one is able to transform any discrete lattice model to an Ising model defined on a (polynomially) larger 2D lattice.Comment: 18 pages, 15 figures, Accepted for publication in Physical Review

To Greener Pastures: An Action Research Study on the Environmental Sustainability of Humanitarian Supply Chains

Purpose: While humanitarian supply chains (HSCs) inherently contribute to social sustainability by alleviating the suffering of afflicted communities, their unintended adverse environmental impact has been overlooked hitherto. This paper draws upon contingency theory to synthesize green practices for HSCs, identify the contingency factors that impact on greening HSCs and explore how focal humanitarian organizations (HOs) can cope with such contingency factors. Design/methodology/approach: Deploying an action research methodology, two-and-a-half cycles of collaboration between researchers and a United Nations agency were completed. The first half-cycle developed a deductive greening framework, synthesizing extant green practices from the literature. In the second and third cycles, green practices were adopted/customized/developed reflecting organizational and contextual contingency factors. Action steps were implemented in the HSC for prophylactics, involving an operational mix of disaster relief and development programs. Findings: First, the study presents a greening framework that synthesizes extant green practices in a suitable form for HOs. Second, it identifies the contingency factors associated with greening HSCs regarding funding environment, stakeholders, field of activity and organizational management. Third, it outlines the mechanisms for coping with the contingency factors identified, inter alia, improving the visibility of headquarters over field operations, promoting collaboration and resource sharing with other HOs as well as among different implementing partners in each country, and working with suppliers for greener packaging. The study advances a set of actionable propositions for greening HSCs. Practical implications: Using an action research methodology, the study makes strong practical contributions. Humanitarian practitioners can adopt the greening framework and the lessons learnt from the implementation cycles presented in this study. Originality/value: This is one of the first empirical studies to integrate environmental sustainability and HSCs using an action research methodology

Completeness of classical ϕ4\phi^4 theory on 2D lattices

We formulate a quantum formalism for the statistical mechanical models of discretized field theories on lattices and then show that the discrete version of $\phi^4$ theory on 2D square lattice is complete in the sense that the partition function of any other discretized scalar field theory on an arbitrary lattice with arbitrary interactions can be realized as a special case of the partition function of this model. To achieve this, we extend the recently proposed quantum formalism for the Ising model \cite{quantum formalism} and its completeness property \cite{completeness} to the continuous variable case.Comment: 20 pages, 8 figures, Accepted for publication in Physical Review