# Bulletin of the American Physical Society

# APS March Meeting 2018

## Monday–Friday, March 5–9, 2018; Los Angeles, California

### Session K45: Helium 4

8:00 AM–10:24 AM,
Wednesday, March 7, 2018

LACC
Room: 505

Sponsoring
Unit:
DCMP

Chair: Gary Williams, Univ of California - Los Angeles

### Abstract: K45.00010 : Critical exponents z and ν for superfluid helium near absolute zero

(Author Not Attending)

#### Presenter:

Vladimir Udodov

(Physics , N. Katanov Khakas State University)

#### Author:

Vladimir Udodov

(Physics , N. Katanov Khakas State University)

We propose a new interpolation formula for the dynamic critical exponent z for the mixture of liquid He4 and He3 at low temperatures:

z=(*d*/2)+[(1+*d*)(1-*S _{I}*)]/(2

*ν*),

*T*→

*T*≥0, α≤0,

_{C}*S*

_{I}*(*

_{ }=*T*/

_{C}*T*)

^{n }, (1)

where

*d*is the space dimension, n is some positive constant [1],

*ν*is the critical exponent of the correlation length, α is the critical exponent of the heat capacity. In the case of

*T*=0 we have

_{C}z=

*d, ν=*(1+

*d*)/

*d, T→T*0 . (2)

_{C}=For

*d*=3 we find

z=3,

*ν=*4/3

*, T→T*0 . (3)

_{C}=This value of z is twice the usual result for T

_{C}>0.

New formulas (1) apply not only to positive critical temperatures but also to the limiting case

*T*→0, which realizes in a mixture of liquid helium isotopes. The results can be applied to the systems with multi-component order parameter, when the thermodynamic potential depends on the sum of the squares of the components. Examples include Heisenberg ferromagnets and systems undergoing quantum phase transitions.

_{C}1. Udodov V.N. New consequences of the static scaling hypothesis at low temperatures. Physics of the Solid State. 2015. 57. 10. . 2073-2077. DOI: 10.1134/S1063783415100340.

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