Properties Of RG Research Articles

Three-loop β function(s) and effective potential in the Gross-Neveu model

We extend the perturbative analysis of the two-dimensional Gross-Neveu model by cimputing within the MS scheme the three-loop renormalization functions β,γ, and γ m in a two-parameter version of the model appropriate to the discussion of the RG properties of the effective potential, whose perturbative expansion is performed to the same order.

Earthquakes, Geology and Crustal Features in Southern New England

Abstract Within southern New england (SNE) and adjacent areas lies a variety of tectonic regions extending from the ancient North American craton to the Avalonian Terrane. This region, which is part of the northern Appalachians, has had a moderate level of seismic activity throughout its recorded history. Although the geology and geophysics of SNE have been studied extensively, it has been difficult to correlate the seismic activity in this region with geologic structures mapped on the earth’s surface. The distribution of earthquakes located by regional seismic networks in SNE generally resembles that of historical earthquakes in this region. In both the network and historical records, a cluster of earthquakes occurs near Moodus, CT and more diffuse seismicity occurs in the eastern coastal regions. Both data sets show earthquake activity in the vicinity of the 1755 earthquake that occurred on the coast of Cape Ann, MA, as well as seismicity near the boundary between southwestern CT and NY State. Aside from these very general similarities, the location uncertainties of the historical earthquakes make it difficult to compare the two records of seismicity in any greater detail. Information about the lateral variation of seismic velocities in the shallow crust beneath SNE has been obtained from studies of dispersion of short-period, fundamental-mode Rayleigh waves (Rg). Rg waves with periods between about 0.2 and 2.5 sec have been studied, and dispersive properties of Rg in that period range are sensitive to lateral variation in the upper few kilometers of the crust. Based on Rg dispersion studies, it appears that SNE can be divided into regions of distinct shallow crustal structure. The pattern of lateral variation is Rg dispersion is similar to the pattern of teleseismic residuals and gravity anomalies, suggesting that the lateral variation revealed by the Rg studies extends deeper into the crust. These results, however, do not reveal any obvious correlations between crustal features and seismicity.