Democrat Hillary Clinton has built a slim lead over Donald Trump in Georgia after one of the worst weeks of the Republican's campaign, and the Libertarian presidential ticket cracked double-digits, according to a new Atlanta Journal-Constitution poll.

The poll released Friday shows Clinton at 44 percent and Trump at 40 percent in a head-to-head matchup, within the poll's margin of error. It is the latest showing a close race between the two candidates in Georgia, a state that has voted for the GOP nominee since 1996.

In a four-way race, Clinton led Trump 41-38, followed by Libertarian Gary Johnson with 11 percent and Green Party candidate Jill Stein with 2 percent. When including which candidates voters "lean" toward, Clinton led Trump 43-39, and Johnson netted 12 percent.

The findings come after both conventions ended and a

, who engaged in a war of words with the family of a slain Muslim U.S. soldier and infuriated many Republicans when he refused to endorse two of the party's top elected officials.

Friday's survey marks a change from the last AJC poll, commissioned in May, which gave Trump a 45-41 lead over Clinton. It also shows the former secretary of state besting Trump among independents, an influential Georgia voting bloc that typically votes Republican.

Both Trump and Clinton had the exact same unfavorability rating - 58 percent - among Georgia voters. And a majority of Trump's backers said they see their decision as a vote against Clinton rather than a vote for the New York businessman.

Johnson barely surpassed 1 percent of Georgia's vote in the 2012 campaign, when he was also the Libertarian nominee for president. But he could be poised to do far better this year by tailoring his pitch to voters disillusioned by both Trump and Clinton, and the poll has him netting about one-fifth of support from Georgia independents.

Georgia still isn't directly in Clinton's crosshairs, and her campaign has yet to declare Georgia a battleground state. But a common strain from the Democratic and Republican conventions was that Georgia has the chance to turn blue for the first time since Bill Clinton's 1992 win over President George H.W. Bush.

The poll was conducted by ABT SRBI between Aug. 1-4 and included 847 registered voters. The margin of error was about 4.3 percentage points.

The AJC will publish several more stories and blog posts about the poll throughout the next few days, so stay tuned.

More: Read all about the AJC poll's findings here.

More: Is this the election that turns Georgia into a battleground state?