scholarly journals Topological Susceptibility under Gradient Flow

2018 ◽  
Vol 175 ◽  
pp. 11024 ◽  
Author(s):  
Héctor Mejía-Díaz ◽  
Wolfgang Bietenholz ◽  
Krzysztof Cichy ◽  
Philippe de Forcrand ◽  
Arthur Dromard ◽  
...  

We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility Xt is measured directly, and by the slab method, which is based on the topological content of sub-volumes (“slabs”) and estimates Xt even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, ξ2). This ongoing study is based on direct measurements of Xt in L × L lattices, at L/ξ ≃6.

Author(s):  
Okuto Morikawa

Abstract The $\mathcal{N}=2$ Landau–Ginzburg description provides a strongly interacting Lagrangian realization of an $\mathcal{N}=2$ superconformal field theory. It is conjectured that one such example is given by the two-dimensional $\mathcal{N}=2$ Wess–Zumino model. Recently, the conjectured correspondence has been studied by using numerical techniques based on lattice field theory; the scaling dimension and the central charge have been directly measured. We study a single superfield with a cubic superpotential, and give an extrapolation method to the continuum limit. Then, on the basis of a supersymmetric-invariant numerical algorithm, we perform a precision measurement of the scaling dimension through a finite-size scaling analysis.


2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.


2018 ◽  
Author(s):  
David M. Rippin

Abstract. We present the first direct measurements of changes taking place at the base of the Getz Ice Shelf (GzIS) in West Antarctica. Our analysis is based on repeated airborne radio-echo sounding (RES) survey lines gathered in 2010 and 2014. We reveal that while there is significant variability in ice shelf behaviour, the vast majority of the ice shelf (where data is available) is undergoing basal thinning at a mean rate of nearly 13 m a−1, which is several times greater than recent modelling estimates. In regions of faster flowing ice close to where ice streams and outlet glaciers join the ice shelf, significantly greater rates of mass loss occurred. Since thinning is more pronounced close to faster-flowing ice, we propose that dynamic thinning processes may also contribute to mass loss here. Intricate sub-ice circulation patterns exist beneath the GzIS because of its complex sub-ice topography and the fact that it is fed by numerous ice streams and outlet glaciers. It is this complexity which we suggest is also responsible for the spatially variable patterns of ice-shelf change that we observe. The large changes observed here are also important when considering the likelihood and timing of any potential future collapse of the ice shelf, and the impact this would have on the flow rates of feeder ice streams and glaciers, that transmit ice from inland Antarctica to the coast. We propose that as the ice shelf continues to thin in response to warming ocean waters and climate, the response of the ice shelf will be spatially diverse. Given that these measurements represent changes that are significantly greater than modelling outputs, it is also clear that we still do not fully understand how ice shelves respond to warming ocean waters. As a result, ongoing direct measurements of ice shelf change are vital for understanding the future response of ice shelves under a warming climate.


Author(s):  
Jean Zinn-Justin

Chapter 7 is devoted to a discussion of the renormalization group (RG) flow when the effective field theory that describes universal properties of critical phenomena depends on several coupling constants. The universal properties of a large class of macroscopic phase transitions with short range interactions can be described by statistical field theories involving scalar fields with quartic interactions. The simplest critical systems have an O(N) orthogonal symmetry and, therefore, the corresponding field theory has only one quartic interaction. However, in more general physical systems, the flow of quartic interactions is more complicated. This chapter examines these systems from the RG viewpoint. RG beta functions are shown to generate a gradient flow. Some examples illustrate the notion of emergent symmetry. The local stability of fixed points is related to the value of the scaling field dimension.


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