Nonperturbative Effects on the Ferromagnetic Transition in Repulsive Fermi Gases
Authors: Lianyi He, Xu-Guang Huang
Abstract
It is generally believed that a dilute spin-1/2 Fermi gas with repulsive interactions can undergo a ferromagnetic phase transition to a spin-polarized state at a critical gas parameter $(k_{\rm F}a)_c$. Previous theoretical predictions of the ferromagnetic phase transition have been based on the perturbation theory, which treats the gas parameter as a small number. On the other hand, Belitz, Kirkpatrick, and Vojta (BKV) have argued that the phase transition in clean itinerant ferromagnets is generically of first order at low temperatures, due to the correlation effects that lead to a nonanalytic term in the free energy. The second-order perturbation theory predicts a first-order phase transition at $(k_{\rm F}a)_c=1.054$, consistent with the BKV argument. However, since the critical gas parameter is expected to be of order O(1), perturbative predictions may be unreliable. In this paper we study the nonperturbative effects on the ferromagnetic phase transition by summing the particle-particle ladder diagrams to all orders in the gas parameter. We consider a universal repulsive Fermi gas where the effective range effects can be neglected, which can be realized in a two-component Fermi gas of $^6$Li atoms by using a nonadiabatic field switch to the upper branch of a Feshbach resonance with a positive s-wave scattering length. Our theory predicts a second-order phase transition, which indicates that ferromagnetic transition in dilute Fermi gases is possibly a counterexample to the BKV argument. The predicted critical gas parameter $(k_{\rm F}a)_c=0.858$ is in good agreement with the recent quantum Monte Carlo result $(k_{\rm F}a)_c=0.86$ for a nearly zero-range potential [S. Pilati, \emph{et al}., Phys. Rev. Lett. {\bf 105}, 030405 (2010)]. We also compare the spin susceptibility with the quantum Monte Carlo result and find good agreement.
The papers around it, by date and closeness
Higher is closer to this paper; left is older. Lines join papers close to each other: groups of lines are sub-topics. Select a point to see why it is there. Back to the summary of this paper
Papers around this one
Ranked by how close their title and abstract are to this paper’s. Select some to read them together.
Closest papers
-
First-order transition and marginal critical behavior in a novel 2D frustrated Ising modelChristophe Chatelain · 2024 · Phys. Rev. E 111, 024109 (2024) · AI summary available
Abstract
The phase diagram of a novel two-dimensional frustrated Ising model with both anti-ferromagnetic and ferromagnetic couplings is studied using Tensor-Network Renormalization-Group techniques. This model can be seen as two anti-ferromagnetic Ising replicas coupled by non-local spin-spin interactions, designed in such a way that the continuum limit matches that of the still debated J1 -J2 model and induces a marginal critical behavior. Our model has the advantage of having more symmetries than the J1 -J2 model and of allowing a more straightforward implementation of Tensor-Network Renormalization-Group algorithms We demonstrate the existence of two transition lines, featuring both first and sec…
-
Thermodynamic crossovers in supercritical fluidsXinyang Li, Yuliang Jin · 2023 · Proceedings of the National Academy of Sciences, 2024, 121(18): e2400313121 · AI summary available
Abstract
Can liquid-like and gas-like states be distinguished beyond the critical point, where the liquid-gas phase transition no longer exists and conventionally only a single supercritical fluid phase is defined? Recent experiments and simulations report strong evidence of dynamical crossovers above the critical temperature and pressure. Despite using different criteria, existing theoretical explanations generally consider a single crossover line separating liquid-like and gas-like states in the supercritical fluid phase. We argue that such a single-line scenario is inconsistent with the supercritical behavior of the Ising model, which has two crossover lines due to its symmetry, violating the univ…
-
Fluctuation-induced spin nematic order in magnetic charge-iceA. Hemmatzade, K. Essafi, M. Taillefumier et al. · 2023 · Statistical Mechanics · AI summary available
Abstract
Disorder in materials may be used to tune their functionalities, but much more strikingly, its presence can entail entirely new behavior. This happens in charge-ice where structural disorder is not weak and local, but strong and long-range correlated. Here, two cations of different charge occupy a pyrochlore lattice, arranging themselves such that all tetrahedra host two cations of each type. The ensuing correlated disorder is characterized by randomly packed loops of a single cation-type. If the cations are magnetic and interact antiferromagnetically, a new type of magnet with strong interactions along the loops, but frustrated interactions between loops, emerges. This results in an ensembl…
-
Finite-Size Scaling of Charge Carrier Mobility in Disordered Organic SemiconductorsPascal Kordt, Thomas Speck, Denis Andrienko · 2015 · Phys. Rev. B 94, 014208 (2016) · Not summarized yet
Abstract
Simulations of charge transport in amorphous semiconductors are often performed in microscopically sized systems. As a result, charge carrier mobilities become system-size dependent. We propose a simple method for extrapolating a macroscopic, nondispersive mobility from the system-size dependence of a microscopic one. The method is validated against a temperature-based extrapolation [Phys. Rev. B 82, 193202 (2010)]. In addition, we provide an analytic estimate of system sizes required to perform nondispersive charge transport simulations in systems with finite charge carrier density, derived from a truncated Gaussian distribution. This estimate is not limited to lattice models or specific ra…
-
System size expansion using Feynman rules and diagramsPhilipp Thomas, Christian Fleck, Ramon Grima et al. · 2014 · Statistical Mechanics · AI summary available
Abstract
Few analytical methods exist for quantitative studies of large fluctuations in stochastic systems. In this article, we develop a simple diagrammatic approach to the Chemical Master Equation that allows us to calculate multi-time correlation functions which are accurate to a any desired order in van Kampen's system size expansion. Specifically, we present a set of Feynman rules from which this diagrammatic perturbation expansion can be constructed algorithmically. We then apply the methodology to derive in closed form the leading order corrections to the linear noise approximation of the intrinsic noise power spectrum for general biochemical reaction networks. Finally, we illustrate our resul…
-
Field Theory of BirhythmicitySergei Shmakov, Peter B. Littlewood · 2025 · Statistical Mechanics · AI summary available
Abstract
Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the fluctuation-dissipation relations as well as the existence of non-static stable states, or phases. A prototypical example is a dynamical phase characterized by a limit cycle - the order parameter of finite magnitude rotating or oscillating at a fixed frequency. Consequently, birhythmicity, where two stable limit cycles coexist, is a natural extension of the simpler single limit cycle phase. Both the abundance of real systems exhibiting such states as well as their …
-
Drift-Controlled Anomalous Diffusion: A Solvable Gaussian ModelFabrizio Lillo, Rosario N. Mantegna · 2000 · Statistical Mechanics · AI summary available
Abstract
We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In particular diffusive, subdiffusive, superdiffusive and stretched exponentially diffusive processes are described by this model for specific values of the two control parameters. The model is also investigated in the presence of an external harmonic potential. We prove that the relaxation to the stationary solution is power-law in time with an exponent controlled by one of model parameters.
-
Diffusion and Relaxation Controlled by Tempered α-stable ProcessesAleksander Stanislavsky, Karina Weron, Aleksander Weron · 2011 · Phys. Rev. E 78, 051106 (2008) · AI summary available
Abstract
We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered \alpha-stable processes. Its most important application is to overcome the infinite-moment difficulty for the \alpha-stable random operational time \tau. The tempering results in the existence of all moments of \tau. The subordination by the inverse tempered \alpha-stable process provides diffusion(relaxation) that occupies an intermediate place between subdiffusion (Cole-Cole law) and normal diffusion (exponential law). Here we obtain explicitly the Fokker-Planck equation, the mean square displacement and the relaxation function. This model includes subdiffusion as a particular case…
Go further
How are these papers found?
We compare the title and abstract of this paper with those of every paper summarized on this site, and with the papers Semantic Scholar recommends, those it cites and those citing it (for a much-cited paper, its most recent citations and, from OpenAlex, the most cited ones). Among the prior work and the follow-ups, the papers that use each other in depth, a method it uses and the much-cited follow-ups come a little higher. The levels (very close, close, related) come from the similarity of the texts, not from a judgment of quality; * marks a paper without an abstract, compared by its title. The sentence under a paper is written by an AI from the two abstracts: check it in the papers. A paper marked not relevant by three readers leaves the list.
For now only among the papers summarized on this site: search again to add the prior work, the follow-ups and Semantic Scholar’s recommendations.