Functional renormalization group approach to the Yang-Lee edge singularity

We determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in $3 \leq d\leq 6$ Euclidean dimensions. We find very good agreement with high-temperature series data in $d = 3$ dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop $\epsilon = 6-d$ expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG $\beta$ functions is discussed and we estimate the error associated with $\mathcal{O}(\partial^4)$ truncations of the scale-dependent effective action.Comment: 10 pages, 4 figures, updated reference to supplementary materia

On spinodal points and Lee-Yang edge singularities

We address a number of outstanding questions associated with the analytic properties of the universal equation of state of the $\phi^4$ theory, which describes the critical behavior of the Ising model and ubiquitous critical points of the liquid-gas type. We focus on the relation between spinodal points that limit the domain of metastability for temperatures below the critical temperature, i.e., $T < T_{\rm c}$, and Lee-Yang edge singularities that restrict the domain of analyticity around the point of zero magnetic field $H$ for $T > T_{\rm c}$. The extended analyticity conjecture (due to Fonseca and Zamolodchikov) posits that, for $T < T_{\rm c}$, the Lee-Yang edge singularities are the closest singularities to the real $H$ axis. This has interesting implications, in particular, that the spinodal singularities must lie off the real $H$ axis for $d < 4$, in contrast to the commonly known result of the mean-field approximation. We find that the parametric representation of the Ising equation of state obtained in the $\varepsilon = 4-d$ expansion, as well as the equation of state of the ${\rm O}(N)$-symmetric $\phi^4$ theory at large $N$, are both nontrivially consistent with the conjecture. We analyze the reason for the difficulty of addressing this issue using the $\varepsilon$ expansion. It is related to the long-standing paradox associated with the fact that the vicinity of the Lee-Yang edge singularity is described by Fisher's $\phi^3$ theory, which remains nonperturbative even for $d\to 4$, where the equation of state of the $\phi^4$ theory is expected to approach the mean-field result. We resolve this paradox by deriving the Ginzburg criterion that determines the size of the region around the Lee-Yang edge singularity where mean-field theory no longer applies.Comment: 26 pages, 8 figures; v2: shortened Sec. 4.1 and streamlined arguments/notation in Sec. 4.2, details moved to appendix, added reference 1

Comparative Study of the Microstructure and Mechanical Properties of Mechanically Alloyed and Spark Plasma Sintered AlxCoCrFeNi (0≤x≤2)High Entropy Alloys

High entropy alloys are a new class of material systems that have promising potential in high temperature structural applications. Mechanical alloying (MA) has gained special attention as a powerful non-equilibrium process for fabricating amorphous and nanocrystalline materials, whereas spark plasma sintering (SPS) is a unique technique for processing dense and near net shape bulk alloys with homogenous microstructure. This research paper discusses novel mechanically alloyed followed by spark plasma sintering approach for assessing composition-microstructure-microhardness relationship in AlxCoCrFeNi (0≤x≤2) high entropy alloy as a candidate system. With increasing Al content, there was a gradual change from a fcc-based microstructure to a bcc-based microstructure (including the ordered B2 phase), accompanied with an increase in microhardness. Such graded alloys are highly attractive candidates for investigating the influence of systematic compositional changes on microstructural evolution and concurrent physical and mechanical properties in complex concentrated alloys or high entropy alloys.https://engagedscholarship.csuohio.edu/u_poster_2018/1073/thumbnail.jp