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Register a new userLocating fixed points in the phase plane
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The critical point is a fixed point in finite-size scaling. To quantify the behaviour of such a fixed point, we define, at a given temperature and scaling exponent ratio, the width of scaled observables for different sizes. The minimum of the width reveals the position of fixed point, its corresponding phase transition temperature, and scaling exponent ratio. The value of this ratio tells the nature of fixed point, which can be a critical point, a point of the first order phase transition line, or a point of the crossover region. To demonstrate the effectiveness of this method, we apply it to three typical samples produced by the 3D three-state Potts model. Results show the method to be more precise and effective than conventional methods. Finally, we discuss a possible application at the beam energy scan program of relativistic heavy-Ion collision.
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If $f:[a,b]to mathbb{R}$, with $a<b$, is continuous and such that $a$ and $b$ are mapped in opposite directions by $f$, then $f$ has a fixed point in $I$. Suppose that $f:mathbb{C}tomathbb{C}$ is map and $X$ is a continuum. We extend the above for certain continuous maps of dendrites $Xto D, Xsubset D$ and for positively oriented maps $f:Xto mathbb{C}, Xsubset mathbb{C}$ with the continuum $X$ not necessarily invariant. Then we show that in certain cases a holomorphic map $f:mathbb{C}tomathbb{C}$ must have a fixed point $a$ in a continuum $X$ so that either $ain mathrm{Int}(X)$ or $f$ exhibits rotation at $a$.
We study fixed points of the easy-plane $mathbb{CP}^{N-1}$ field theory by combining quantum Monte Carlo simulations of lattice models of easy-plane SU($N$) superfluids with field theoretic renormalization group calculations, by using ideas of deconfined criticality. From our simulations, we present evidence that at small $N$ our lattice model has a first order phase transition which progressively weakens as $N$ increases, eventually becoming continuous for large values of $N$. Renormalization group calculations in $4-epsilon$ dimensions provide an explanation of these results as arising due to the existence of an $N_{ep}$ that separates the fate of the flows with easy-plane anisotropy. When $N<N_{ep}$ the renormalization group flows to a discontinuity fixed point and hence a first order transition arises. On the other hand, for $N > N_{ep}$ the flows are to a new easy-plane $mathbb{CP}^{N-1}$ fixed point that describes the quantum criticality in the lattice model at large $N$. Our lattice model at its critical point thus gives efficient numerical access to a new strongly coupled gauge-matter field theory.
We present a top-down string theory holographic model of strongly interacting relativistic 2+1-dimensional fermions, paying careful attention to the discrete symmetries of parity and time reversal invariance. Our construction is based on probe $D7$-branes in $AdS_5 times S^5$, stabilized by internal fluxes. We find three solutions, a parity and time reversal invariant conformal field theory which can be viewed as a particular deformation of Coulomb interacting graphene, a parity and time reversal violating but gapless field theory and a system with a parity and time reversal violating charge gap. We show that the Chern-Simons-like electric response function, which is generated perturbatively at one-loop order by parity violating fermions and which is protected by a no-renormalization theorem at orders beyond one loop, indeed appears with the correctly quantized coefficient in the charge gapped theory. In the gapless parity violating solution, the Chern-Simons response function obtains quantum corrections which we compute in the holographic theory.
In supersymmetric models with scalar sequestering, superconformal strong dynamics in the hidden sector suppresses the low-energy couplings of mass dimension two, compared to the squares of the dimension one parameters. Taking into account restrictions on the anomalous dimensions in superconformal theories, I point out that the interplay between the hidden and visible sector renormalizations gives rise to quasi-fixed point running for the supersymmetric Standard Model squared mass parameters, rather than driving them to 0. The extent to which this dynamics can ameliorate the little hierarchy problem in supersymmetry is studied. Models of this type in which the gaugino masses do not unify are arguably more natural, and are certainly more likely to be accessible, eventually, to the Large Hadron Collider.
We report on an intriguing observation that the values of all the couplings in the standard model except those related to first two generations can be understood from the IR fixed point structure of renormalization group equations in the minimal supersymmetric model extended by one complete vectorlike family with the scale of new physics in a multi-TeV range.
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