Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userIsobaric Critical Exponents: Test of Analyticity against NIST Reference Data
66
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Finite systems may undergo first or second order phase transitions under not isovolumetric but isobaric condition. The `analyticity of a finite-system partition function has been argued to imply universal values for isobaric critical exponents, $alpha_{{scriptscriptstyle{P}}}$, $beta_{{scriptscriptstyle{P}}}$ and $gamma_{{scriptscriptstyle{P}}}$. Here we test this prediction by analyzing NIST REFPROP data for twenty major molecules, including $mathrm{H_{2}O, CO_{2}, O_{2}}$, etc. We report they are consistent with the prediction for temperature range, $10^{-5} <|T/T_{c}-1|<10^{-3}$. For each molecule, there appears to exist a characteristic natural number, $n=2,3,4,5,6$, which determines all the critical exponents for $T<T_{c}$ as $alpha_{{scriptscriptstyle{P}}}=gamma_{{scriptscriptstyle{P}}}=frac{n}{n+1}$ and $beta_{{scriptscriptstyle{P}}}=delta^{-1}=frac{1}{n+1}$. For the opposite $T>T_{c}$, all the fluids seem to indicate the universal value of ${n=2}$.
rate research
Read More
The critical behaviour of d-dimensional n-vector models at m-axial Lifshitz points is considered for general values of m in the large-n limit. It is proven that the recently obtained large-N expansions [J. Phys.: Condens. Matter 17, S1947 (2005)] of the correlation exponents eta_{L2}, eta_{L4} and the related anisotropy exponent theta are fully consistent with the dimensionality expansions to second order in epsilon=4+m/2-d [Phys. Rev. B 62, 12338 (2000); Nucl. Phys. B 612, 340 (2001)] inasmuch as both expansions yield the same contributions of order epsilon^2/n.
We present mathematical details of derivation of the critical exponents for the free energy and magnetization in the vicinity of the Gaussian fixed point of renormalization. We treat the problem in general terms and do not refer to particular models of interaction energy. We discuss the case of arbitrary dispersion of the fixed point.
Renormalization group theory does not restrict the from of continuous variation of critical exponents which occurs in presence of a marginal operator. However, the continuous variation of critical exponents, observed in different contexts, usually follows a weak universality scenario where some of the exponents (e.g., $beta, gamma, u$) vary keeping others (e.g., $delta , eta$) fixed. Here we report a ferromagnetic phase transition in (Sm$_{1-y}$Nd$_{y}$)$_{0.52}$Sr$_{0.48}$MnO$_3$ $(0.5le yle1)$ single crystal where all critical exponents vary with $y.$ Such variation clearly violates both universality and weak universality hypothesis. We propose a new scaling theory that explains the present experimental results, reduces to the weak universality as a special case, and provides a generic route leading to continuous variation of critical exponents and multicriticality.
The paramagnetic-to-ferromagnetic phase transition is believed to proceed through a critical point, at which power laws and scaling invariance, associated with the existence of one diverging characteristic length scale -- the so called correlation length -- appear. We indeed observe power laws and scaling behavior over extraordinarily many decades of the suitable scaling variables at the paramagnetic-to-ferromagnetic phase transition in ultrathin Fe films. However, we find that, when the putative critical point is approached, the singular behavior of thermodynamic quantities transforms into an analytic one: the critical point does not exist, it is replaced by a more complex phase involving domains of opposite magnetization, below as well as $above$ the putative critical temperature. All essential experimental results are reproduced by Monte-Carlo simulations in which, alongside the familiar exchange coupling, the competing dipole-dipole interaction is taken into account. Our results imply that a scaling behavior of macroscopic thermodynamic quantities is not necessarily a signature for an underlying second-order phase transition and that the paramagnetic-to-ferromagnetic phase transition proceeds, very likely, in the presence of at least two long spatial scales: the correlation length and the size of magnetic domains.
We study the pair contact process with diffusion (PCPD) using Monte Carlo simulations, and concentrate on the decay of the particle density $rho$ with time, near its critical point, which is assumed to follow $rho(t) approx ct^{-delta} +c_2t^{-delta_2}+...$. This model is known for its slow convergence to the asymptotic critical behavior; we therefore pay particular attention to finite-time corrections. We find that at the critical point, the ratio of $rho$ and the pair density $rho_p$ converges to a constant, indicating that both densities decay with the same powerlaw. We show that under the assumption $delta_2 approx 2 delta$, two of the critical exponents of the PCPD model are $delta = 0.165(10)$ and $beta = 0.31(4)$, consistent with those of the directed percolation (DP) model.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
