7,719 research outputs found

    Singular limits of reaction diffusion equations and geometric flows with discontinuous velocity

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    We consider the singular limit of a bistable reaction diffusion equation in the case when the velocity of the traveling wave solution depends on the space variable and converges to a discontinuous function. We show that the family of solutions converges to the stable equilibria off a front propagating with a discontinuous velocity. The convergence is global in time by applying the weak geometric flow uniquely defined through the theory of viscosity solutions and the level-set equation

    Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at Q>4Q>4

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    We study complex CFTs describing fixed points of the two-dimensional QQ-state Potts model with Q>4Q>4. Their existence is closely related to the weak first-order phase transition and walking RG behavior present in the real Potts model at Q>4Q>4. The Potts model, apart from its own significance, serves as an ideal playground for testing this very general relation. Cluster formulation provides nonperturbative definition for a continuous range of parameter QQ, while Coulomb gas description and connection to minimal models provide some conformal data of the complex CFTs. We use one and two-loop conformal perturbation theory around complex CFTs to compute various properties of the real walking RG flow. These properties, such as drifting scaling dimensions, appear to be common features of the QFTs with walking RG flows, and can serve as a smoking gun for detecting walking in Monte Carlo simulations. The complex CFTs discussed in this work are perfectly well defined, and can in principle be seen in Monte Carlo simulations with complexified coupling constants. In particular, we predict a pair of S5S_5-symmetric complex CFTs with central charges c1.138±0.021ic\approx 1.138 \pm 0.021 i describing the fixed points of a 5-state dilute Potts model with complexified temperature and vacancy fugacity.Comment: 34 pages, 13 figures. v2: refs added; v3 refs added, typos corrected, presentation of several arguments clarifie

    Walking, Weak first-order transitions, and Complex CFTs

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    We discuss walking behavior in gauge theories and weak first-order phase transitions in statistical physics. Despite appearing in very different systems (QCD below the conformal window, the Potts model, deconfined criticality) these two phenomena both imply approximate scale invariance in a range of energies and have the same RG interpretation: a flow passing between pairs of fixed point at complex coupling. We discuss what distinguishes a real theory from a complex theory and call these fixed points complex CFTs. By using conformal perturbation theory we show how observables of the walking theory are computable by perturbing the complex CFTs. This paper discusses the general mechanism while a companion paper [1] will treat a specific and computable example: the two-dimensional Q-state Potts model with Q > 4. Concerning walking in 4d gauge theories, we also comment on the (un)likelihood of the light pseudo-dilaton, and on non-minimal scenarios of the conformal window termination.Comment: 38 pages, added reference

    Importance of documentary credit in international trade: analysis of risk and prevention measures

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    Dissertação de mestrado em International BusinessIn international trade settlement, letters of credit (documentary credit), documentary collections, and remittances are generally accepted international settlement methods. Letters of credit take the leading position, with the characteristics of bank credit and the reciprocal rights and obligations of buyer and seller. It has the function of guaranteeing security to both exporters and importers; therefore, it is relatively safe means of settlement, which guarantees the adequate functioning of international transactions. However, due to their characteristics, letters of credit are not exempt from risks in their practical application. Therefore, the study of the risk and preventive measures of the letter of credit has a strong relevance to the practice of international trade. This dissertation mainly analyzes the risk that the applicant, the bank (issuing bank and negotiating bank) and the beneficiary may face in the process of using the credit, and puts forward the corresponding risk prevention measures. Using a qualitative approach, we found a unique perspective and new findings on the risk and risk prevention measures. The results of this exploratory study suggest that there is a consensus in considering the principle of letter of credit independence as one of its main sources of risk. This consensus suggests that future development of the letter of credit involves reducing their independence, without completely losing its independence essence. The evolution of letters of credit may also include the cooperative development of operations and the use of digital platforms to facilitate the investigation of the credibility of business partners.No comércio internacional, letras de crédito (crédito documentário), cobranças documentárias e remessas são os métodos de pagamento geralmente aceites. A letra de crédito assume a posição de liderança enquanto forma de pagamento no comércio internacional com as características do crédito bancário e os direitos e obrigações recíprocos do comprador e do vendedor. Tem a função de garantir a segurança a importadores e exportadores, sendo uma forma de liquidação relativamente segura, que garante a condução normal das transações internacionais. No entanto, pelas suas características, as letras de crédito não estão isentas de risco na sua aplicação prática. Portanto, o estudo do risco e das medidas preventivas do risco da carta de crédito tem uma forte relevância para a prática comercial internacional. Esta dissertação analisa principalmente o risco que o ordenador (comprador), os bancos (banco emitente e banco negociador) e o beneficiário (vendedor) podem enfrentar no processo de utilização das letras de crédito e discute as correspondentes medidas de prevenção de risco. Com base numa abordagem qualitativa, foi possível obter uma perspetiva prática sobre os riscos e as correspondentes medidas de prevenção de risco. Os resultados deste estudo exploratório sugerem que existe um consenso em considerar o princípio da independência da carta de crédito como uma das suas principais fontes de risco. Esse consenso sugere que o desenvolvimento futuro da letra de crédito deverá passar por reduzir a sua independência, mas sem perder completamente a sua essência de independência. A evolução também deverá incluir o desenvolvimento cooperativo das operações e o uso das plataformas digitais para facilitar a investigação da credibilidade dos parceiros de negócios

    Non-gaussianity of the critical 3d Ising model

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    We discuss the 4pt function of the critical 3d Ising model, extracted from recent conformal bootstrap results. We focus on the non-gaussianity Q - the ratio of the 4pt function to its gaussian part given by three Wick contractions. This ratio reveals significant non-gaussianity of the critical fluctuations. The bootstrap results are consistent with a rigorous inequality due to Lebowitz and Aizenman, which limits Q to lie between 1/3 and 1.Comment: 10 pages, 6 figures; v2: refs added; v3: refs updated, published version; v4: acknowledgement adde
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