A study of the renormalization group flow in the three-dimensional nonlinear O(N) sigma model using Monte Carlo Renormalization Group (MCRG) techniques is presented. To achieve this, we combine an improved blockspin transformation with the canonical demon method to determine the flow diagram for a number of different truncations. Systematic errors of the approach are highlighted. Results are discussed with hindsight on the fixed point structure of the model and the corresponding critical exponents. Special emphasis is drawn on the existence of a nontrivial ultraviolet fixed point as required for theories modeling the asymptotic safety scenario of quantum gravity.

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Supersymmetry is a prominent candidate for physics beyond the standard model. In order to compute the spectrum of supersymmetric theories, we employ nonperturbative lattice QFT techniques which due to the discretisation of spacetime violate supersymmetry at finite lattice spacings. Care has to be taken then to restore supersymmetry in the continuum limit. We discuss a discretisation of the supersymmetric Nonlinear O(N) Sigma model in two dimensions and argue that supersymmetry may be restored by finetuning of a single parameter. Furthermore, we show preliminary results for the vacuum physics of N = 2 Super-Yang-Mills theory in three dimensions.

Current strategies to simulate dynamic behavior of large molecular systems involve computationally expensive fully atomistic models, or lower resolution models that have been coarsened. Coarsening is accomplished by grouping tightly bonded atoms, with little relative motion, in two main ways: spherical beads, and rigid bodies. The latter method, which preserves system geometry, has been shown to better capture the system physics by including rotational equations of motion of the coarsened region. This can have a significant effect on the system dynamics. The most advanced of these methods adaptively determine the regions that should be coarsened, and approach O(log(n)) computational performance (n is the number of coarsened regions in the system). Low computational order methods are limited by the pairwise force computation at each time step, which is required for biochemical systems. Thus, an approximation has been proposed for use with these methods that reduce the computational complexity of the force computation to O(nlog(n)). This approximation method (constructed similarly to the Fast Multipole Method) requires that the minimum distance between coarsened regions be computed. Intuitively obvious strategies, such as tracking the exact system geometry, are often so expensive that they negate the benefits of using a reduced order method. To this end, pseudo-radius of gyration is proposed that is computed from a tensor quantity similar to the inertia tensor, but describes the charge distribution of the coarsened region. The mechanisms for manipulating this quantity during the assembly and disassembly of coarsened regions would be similar to what is done for the actual inertia tensor in the current dynamics model. This quantity will be computationally inexpensive to store and manipulate, therefore will preserve the overall low computational cost of the force approximation, while allowing for a more accurate coarsening strategy.

Supersymmetry is a prominent candidate for physics beyond the standard model. In order to compute the spectrum of supersymmetric theories, we employ nonperturbative lattice QFT techniques which due to the discretisation of spacetime violate supersymmetry at finite lattice spacings. Care has to be taken then to restore supersymmetry in the continuum limit. We discuss a discretisation of the supersymmetric Nonlinear O(N) Sigma model in two dimensions and argue that supersymmetry may be restored by finetuning of a single parameter. Furthermore, we show preliminary results for the vacuum physics of N = 2 Super-Yang-Mills theory in three dimensions.